user471: As I understand, once someone attains Nirvana and passes away, there is no more dependant arising, meaning this person no longer manifests as a person or being in any realm. This also means that this person loses his personhood (although this personhood is impermanent and is part of dukkha).
On the other hand, by achieving the first four Jhanas, a person could be reborn in the Brahma realms, which I understand to be the best beings in the universe, besides the Bodhisattvas. Of course, this is still impermanent and part of dukkha, but one could keep trying over and over to be reborn again and again in the Brahma realms.
The other possibility is to become a (Mahayana) Bodhisattva, in which case one maintains his personhood also. Although a Bodhisattva is destined to become a Buddha.
The question is, why should sentient beings choose to end their personhood permanently, rather than trying to be reborn again and again as the best person possible?

user801: "Of course, this is still impermanent and part of dukkha, but one could keep trying over and over to be reborn again and again in the Brahma realms." - Well, but it's not completely under your control - it may well happen that when one falls from a Brahma Realm and is reborn in a lower - one forgets about one's past life and one's bad karma having matured - one's intention is no longer pure (Moreover, the circumstances one is reborn in may be exceptionally disagreeable/unfavorable for treading the Path of Purity - depending on one's karma of course). I think the following story should make this point clear.

IN BRAHMA LAND HE SHINES BRIGHT; IN PIG'S PEN, TOO, HE FINDS DELIGHT
At one time, the Blessed One went into Rãjagiri for almsround. On
  seeing a young female pig, the Blessed One smiled. Noticing the white
  radiation which shone forth from the teeth of the Buddha, the
  Venerable Ànandã knew that the Buddha was smiling. Accordingly, he
  asked: "What has caused, Sire, to smile?"
The Blessed One pointed out the young female pig to Ànandã and said,
  "See that young female pig? She was a young woman in human existence
  during the dispensation of Kakusanda Buddha. When she died, she was
  reborn a hen in the neighbourhood of a monastic feeding hall. The
  small hen fell victim to an eagle. But earlier she happened to have
  heard the recitation by a yogi Buddhist monk of a meditation subject
  which aroused in her wholesome thoughts. By virtue of these merits,
  the small hen was reborn as a princess named Ubbari in a royal family.
  The princess Ubbari later left the household life and became a
  wandering mendicant. Residing in the mendicants' residence she
  happened one day to gaze at the maggots in the latrine. The worms
  served as an object for meditation (contemplation of ugliness of
  worm-infested corpse or contemplation of a white object) by which she
  attained the first jhãna. When she passed away, she was reborn a
  Brahma in the first jhãnic Brahma world. On expiry from the Brahma
  world, she became the daughter of a rich man in the human world which
  she left again only to be born a pig now. I saw all these events which
  made me smile."
On hearing this story of repeated births in various existences,
  Venerable Ànandã and other monks became greatly alarmed and agitated
  with religious emotion. The Blessed One stopped going on alms-round
  and while still standing on the roadway, started teaching the dhamma
  in six verses, the first one of which stated:
Yathãpi móle anupaddove dalhe,
chinnopi rukho punareva róhati
evaõpi tanhã nusaye anuhate
nibbattati dukkhamidaõ punappunam

'If the main roots of a tree remain undamaged and in good condition,
  even when the upper branches are cut off that tree will grow again
  developing new buds and shoots. Likewise, if there remains defilements
  (lying dormant) which are not yet eradicated by ariya magga, this
  suffering of rebirth will arise time and again successively.'
What is conveyed by this verse is this: 'During her existence as
  princess Ubbari, she renounced the world to become a wanderer. By
  practising meditation, she attained the first jhãna which could dispel
  or put away by vikkhambhana pahãna (elimination by discarding) only
  the defilements of pariyutthana class, i.e. craving for sensual
  pleasure which appears as sensuous thoughts at the mind's door. By
  means of vikkhambhana pahãna, jhãna can put away the defilements only
  to a certain distance for a certain period of time. Thus, she was able
  to dispel the craving for sensual pleasure when she attained the first
  jhãna and later in the Brahma world. But when she was born again in
  the human world as the daughter of a wealthy man, the craving for
  sensual pleasure reappeared because it had not been rooted out by the
  ariya magga. The bhava tanhã (craving for existence), of course,
  persisted even when she had attained the jhãna. Because the latent
  defilements had not been completely uprooted, she had to descend from
  the Brahma world, through the human world, into a pig's existence. So
  long as the craving persists, repeated rebirths will take place in
  this way in various existences.'
In reference to this story of descent from the Brahma world to a pig's
  existence, ancient Sayadaws had left an aphorism, 'In Brahma land, she
  shines bright; in pig's pen, too, she finds delight'. But it is not
  possible to be reborn as a pig straight from the Brahma world, nor as
  any other animal nor in the realms of petas (starving ghosts) nor in
  the states of misery. By virtue of the upacãra bhãvanã, the access
  meditation, proximate to the jhãna previously attained, rebirth can
  take place only as a human being or in the celestial abode. The young
  female pig of the above story also passed through human life where she
  was born as the daughter of a wealthy man. It is quite possible that
  she landed in a pig's existence after being the daughter of a wealthy
  man because of the bad kamma she had committed then, in being haughty
  and insolent to those she should have shown respect.
When the young female pig died, she was reborn in a royal family of
  Suvannabhumi, which is generally taken to be the country of Thaton.
  Some scholars, however, take Suvannabhumi to be the Sumatra island,
  relying on the bronze inscriptions made by the King Devapala about
  1500 Buddhist era.
From being a princess of Suvannabhumi, she passed over to Varanasi,
  India, as a woman. She then became a woman in Varãnasi, in south-east
  of Bombay. From there, she was reborn the daughter of a horse-merchant
  in the seaport town of Supparaka, north-west of Bombay. Next, she
  became the daughter of a shipowner at the port of Kavira in the
  south-easternmost part of the Indian peninsular. This is the coastal
  district inhabited by the Tamil people, formerly called Damila. After
  that life, she was reborn in the family of a government official at
  Anuradha or present day Sri Lanka. Her next life was as a daughter of
  a rich man, named Sumana from Bhokkanta, a village south of Anuradha.
  She took the same name as her father, Sumana. Later her father left
  that village and settled down in the Mahãmuni village of the Dighavapi
  District. One day, a minister of the king Dutthagãmini, named
  Lakundala Atimbara, happened to visit the Mahamuni village on a
  certain business. Upon seeing the young lady Sumana, he fell madly in
  love with her. He married her with great pomp and ceremony and carried
  her off to his village, Mahãpunna.
The Venerable Mahã Anuruddha, who resided at the monastery of
  Taungsun, happened to visit her village for alms-round. While waiting
  for offer of almsfood at the gate of Sumana's house, he saw Sumana and
  said to his monk followers: "Bhikkhus, how wonderful, what a marvel!
  The young female pig of the Blessed One's time is now the wife of the
  minister Lakundaka Atimbara."
On hearing this exclamation, Sumana, the wife of the minister,
  developed jatissara ñãna (knowledge of previous existences). With the
  help of this faculty, she recalled to her mind the previous existences
  she had passed through. In consequence, she became agitated with fear
  at the prospect of repeated births in the cycle of existences. Asking
  permission from her minister husband, she went to a bhikkhuni
  monastery and got herself ordained. After ordination, she listened to
  the discourse on Satipaööhãna Sutta at Tissa Mahã Vihãra monastery.
  Practising mindfulness meditation in accordance with the sutta, she
  became a sotapanna, well-established as a stream-winner in the first
  stage of the Path and Fruition. Then, when king Dutthagamini came on
  the throne, she went back to her native village, Bhokkanta, where at
  the Kalla Mahã Vihãra monastery she heard the discourse on Asivisopana
  Sutta which enabled her to attain the fourth stage of the Fruition and
  became an Arahat, completely free from influxes, passions.
Going over the thirteen existences of Sumana thoughtfully and
  mindfully, one could get aroused with religious emotion. When, as the
  young woman at the time of the Kakusanda Buddha died, she left behind
  her family, possessions and her own physical body. The bereft family
  and friends would have grieved over her death. She became a hen. What
  a frightful thought, a human being to be reborn a hen! That hen would
  have a family and friends, too. She met with a terrible death, from
  decapitation, when an eagle seized her and struck her fiercely with
  its beak. There is consolation, however, that she was reborn a
  princess for the merit accrued from having heard a discourse on
  meditation. The hen would not, of course, know anything of the dhamma,
  but as she had given devout attention to the discourse, certain merit
  would have accrued to her for which she was reborn a princess.
  Listening to a dhamma discourse is thus very beneficial and fruitful.
It is a matter for gratification that she became a Brahma after being
  a princess by virtue of her jhãnic attainments. It is gratifying too
  that from the Brahma world she was reborn in the human world into a
  wealthy family. But it is very distressing to know that she left
  behind her family, friends and possessions reluctantly to be reborn a
  female pig. It is really frightful to think of descending to human
  plane from the Brahma world and to sink further still into animal
  kingdom as a pig. This should be enough to excite alarm and religious
  emotion because so long as the noble ariya magga has not been
  established, anyone is liable to find himself landed in lowly states
  of existence. It was with the intention of arousing religious emotions
  and exhorting the bhikkhus to take to dhamma in all earnestness that
  the Blessed One had told them the account of the female hen's
  succession of existences.
How the young female pig met her death was not mentioned in the texts,
  but it could be presumed that she was slaughtered by her breeder as in
  modern times. The young female pig must have had a family and friends
  which she left behind, causing grief to them. It was comforting that
  she was reborn afterwards as a human being in six places from
  Suvannabhómi to Anurãdha. But in each of these existences, every time
  she departed from one life there must have been considerable suffering
  from sorrow, lamentation and grief for her and her dear ones. That she
  finally became Bhikkhuni Sumana Theri is the most heartening part of
  the story.
The cause of the succession of her existences departing from one life
  to be reborn in another is tanhã or samudaya saccã, the Truth of the
  Origin of Suffering. Other people who are not yet rid of tanhã will
  likewise go through the cycle of rebirths, dying from one life to be
  reborn in another. It is extremely important, therefore, to get
  established in the practice of the Noble Ariyan Path in order to
  eradicate tanhã, otherwise called the Truth of the Origin of
  Suffering. Sumana Theri first heard the discourse on Satipatthãna
  Sutta. Then she practised mindfulness in accordance with the
  Satipatthãna method which helped her attain the status of sotapanna
  (the stream-winner). Then, hearing the Asivisopana Sutta, she devoted
  herself more ardently to the practice and attained Arahatta Fruition
  to become a female Arahat. Tanhã, otherwise samudaya, was completely
  eradicated from her. Therefore, there would be no more rebirth for her
  and she would be enjoying peace after her parinibbana.
Sumana Theri, therefore, declared to her colleagues that she would
  fully pass away (parinibbhuto) after the ayusaïkhãra, the vital
  principle for her present existence had become exhausted. Thereupon,
  her colleagues, bhikkhus and bhikkhunis requested of her the story of
  her existences. "I was a human woman at the time of the Kakusanda
  Buddha. When I died from there, I became a hen. I was killed by an
  eagle which broke off my head and devoured me. Then I became a
  princess in the human world . . ." she continued to recount her past
  existences till the time of her final existence at Bhokkanta village.
  She concluded, "Thus have I passed through thirteen existences
  encountering the ups and downs, vicissitudes of life in each
  existence. In this last existence, being wearied of the cycle of
  rebirths, I have become an ordained bhikkhuni and finally attained
  Arahatship. I urge all of you, my righteous bhikkhus and bhikkhunis,
  to put forth your endeavour mindfully to become fully accomplished in
  sila, samãdhi and paññã." Then she passed away, causing religious
  agitation in the minds of her audience, consisting of men, women,
  bhikkhus and bhikkhunis. This story of the young female pig is fully
  described in the commentary to the Dhammapada.

And of course - the important thing to realize is that the Brahmas Realms or even Bodhisattas are still not completely free from suffering - So, it is important ask oneself - Why would one wish to be content with a lesser amount of suffering - when the complete cessation of suffering has been declared to the world by the Tathagata ?
You can read in greater detail about rebirth and dependent-origination here :
http://www.buddhanet.net/wheeld05.htm
This is how the Buddha compares rebirth in the Brahma Realm with Nibbana :

Sariputta : "What do you think, Dhanañjanin? Which is better: hell or the animal
  womb?"
"The animal womb is better than hell, Master Sariputta."
"... Which is better: the animal womb or the realm of the hungry
  shades?"
"... the realm of the hungry shades..."
"... the realm of the hungry shades or human beings?"
"... human beings..."
"...human beings or the Four Great King devas?"
"...the Four Great King devas..."
"...the Four Great King devas or the devas of the Thirty-three?"
"...the devas of the Thirty-three..."
"...the devas of the Thirty-three or the Yama devas?"
"...the Yama devas..."
"...the Yama devas or the Tusita devas?"
"...the Tusita devas..."
"...the Tusita devas or the Nimmanarati devas?"
"...the Nimmanarati devas..."
"...the Nimmanarati devas or the Paranimmitavasavatti devas?"
"...the Paranimmitavasavatti devas..."
"...the Paranimmitavasavatti devas or the Brahma world?"
"Did Master Sariputta say, 'Brahma world'? Did Master Sariputta say,
  'Brahma world'?"
Then the thought occurred to Ven. Sariputta, "These brahmans are set
  on the Brahma world. What if I were to teach Dhanañjanin the brahman
  the path to union with the Brahmas?"
[So he said:] "Dhanañjanin, I will teach you the path to union with
  the Brahmas. Listen and pay careful attention to that. I will speak."
"As you say, master," Dhanañjanin the brahman responded to Ven.
  Sariputta.
Ven. Sariputta said: "And what is the path to union with the Brahmas?
  There is the case where a monk keeps pervading the first direction
  [the east] with an awareness imbued with good will, likewise the
  second, likewise the third, likewise the fourth. Thus above, below, &
  all around, everywhere, in its entirety, he keeps pervading the
  all-encompassing cosmos with an awareness imbued with good will —
  abundant, expansive, immeasurable, without hostility, without ill
  will. He keeps pervading the first direction with an awareness imbued
  with compassion ... appreciation ... equanimity, likewise the second,
  likewise the third, likewise the fourth. Thus above, below, & all
  around, everywhere, in its entirety, he keeps pervading the
  all-encompassing cosmos with an awareness imbued with equanimity —
  abundant, expansive, immeasurable, without hostility, without ill
  will. This, Dhanañjanin, is the path to union with the Brahmas."
"In that case, Master Sariputta, pay homage to the Blessed One's feet
  with your head in my name and say 'Lord, Dhanañjanin the brahman is
  diseased, in pain, severely ill. He pays homage with his head to the
  Blessed One's feet.'"
So Ven. Sariputta — when there was still more to be done, having
  established Dhanañjanin the brahman in the inferior Brahma world —
  got up from his seat and left. Then, not long after Ven. Sariputta's
  departure, Dhanañjanin the brahman died and reappeared in the Brahma
  world.
And the Blessed One said to the monks, "Monks, Sariputta — when there
  was still more to be done, having established Dhanañjanin the brahman
  in the inferior Brahma world — has gotten up from his seat and left."
Then Ven. Sariputta went to the Blessed One and, on arrival, having
  bowed down to him, sat to one side. As he was sitting there he said to
  the Blessed One, "Lord, Dhanañjanin the brahman is diseased, in pain,
  severely ill. He pays homage with his head to the Blessed One's feet."
"But why, Sariputta — when there was still more to be done, having
  established Dhanañjanin the brahman in the inferior Brahma world — did
  you get up from your seat and leave?"
"The thought occurred to me, lord, 'These brahmans are set on the
  Brahma worlds. What if I were to teach Dhanañjanin the brahman the
  path to union with the Brahmas?'"
"Sariputta, Dhanañjanin the brahman has died and reappeared in the
  Brahma world."
Dhanañjāni Sutta (MN 97) 


user-1: "[...] This also means that this person loses his personhood (although this personhood is impermanent and is part of dukkha)."
I wouldn't say "loses". It may be worth reminding that Nirvana should not be considered annihilation. Complementing:

Bhikkhus, it is impossible that a bhikkhu who considers nibbāna to be suffering will possess a conviction in conformity [with the teaching]. [...] [But] it is possible that a bhikkhu who considers nibbāna to be hapiness will possess a conviction in conformity [with the teaching].
-- Nibbāna [Bodhi Trans.], AN 6:101

"On the other hand, by achieving the first four Jhanas, a person could be reborn in the Brahma realms, which I understand to be the best beings in the universe, besides the Bodhisattvas."
Personal preferences aside, if we are talking about happiness, Nibbāna is declared to be supreme. A happiness and security from suffering unknown to a Brahma or Bodhisattva.
Also, perhaps is not so surprising the idea of devas of superior realms desiring to be born as humans:

"It's a gain for you, monks, a great gain, that you've gained the opportunity to live the holy life. I have seen a heaven named 'Six Spheres of Contact.' Whatever form one sees there with the eye is desirable, never undesirable; pleasing, never displeasing; agreeable, never disagreeable. Whatever sound one hears there with the ear... Whatever aroma one smells there with the nose... Whatever flavor one tastes there with the tongue... Whatever tactile sensation one touches there with the body... Whatever idea one cognizes there with the intellect is desirable, never undesirable; pleasing, never displeasing; agreeable, never disagreeable.
-- Khana Sutta, SN 35.135

"[...] but one could keep trying over and over to be reborn again and again in the Brahma realms."
...and, while trying, out of inattention or forgetfulness or simply ignorance, one may do something foolish -- because that's what we do as ignorants. Foolish enough to open one's mind to darker unwholesome states, perhaps in a chain reaction, and end up in a worse destination (though reappearing as a human during a time with no dhamma, and no condition to develop oneself to become a Buddha might be bad enough). Perhaps you were Brahma before, and now here you are, among humans (again?). I guess, as long as one thinks this endeavor is worth...
"The question is, why should sentient beings choose to end their personhood permanently, rather than trying to be reborn again and again as the best person possible?"
One way of answering is to ask "What's to end?".
Here is an appeal from the Buddha himself as to why one should reach Nirvana:

"Bhikkhus, this samsāra is without discoverable beginning. A first point is not discerned of beings roaming and wandering on hindered by ignorance and fettered by craving. What do you think, bhikkhus, which is more: the stream of tears that you have shed as you roamed and wandered on through this long course, weeping and wailing because of being united with the disagreeable and separated from the agreeable -- this or the water in the four great oceans?"
"[...] venerable sir, [...] this alone is more than the water in the four great oceans."
"Good, good, bhikkhus! It is good that you understand the Dhamma taught by me in such a way. [...] For a long time, bhikkhus, you have experienced the death of a father ... the death of a brother ... the death of a sister ... the death of a daughter ... the loss of relatives ... the loss of wealth ... the loss through illness [...]. For what reason? Because, bhikkhus, this samsāra is without discoverable beginning ... It is enough to experience revulsion towards all formations, enough to become dispassionate towards them, enough to be liberated from them."
-- Tears [Bodhi Trans.], SN 15.3


471: <p>As I understand, once someone attains Nirvana and passes away, there is no more dependant arising, meaning this person no longer manifests as a person or being in any realm. This also means that this person loses his personhood (although this personhood is impermanent and is part of dukkha).</p>

<p>On the other hand, by achieving the first four Jhanas, a person could be reborn in the Brahma realms, which I understand to be the best beings in the universe, besides the Bodhisattvas. Of course, this is still impermanent and part of dukkha, but one could keep trying over and over to be reborn again and again in the Brahma realms.</p>

<p>The other possibility is to become a (Mahayana) Bodhisattva, in which case one maintains his personhood also. Although a Bodhisattva is destined to become a Buddha.</p>

<p>The question is, why should sentient beings choose to end their personhood permanently, rather than trying to be reborn again and again as the best person possible?</p>
 801: <p>"Of course, this is still impermanent and part of dukkha, but one could keep trying over and over to be reborn again and again in the Brahma realms." - Well, but it's not completely under your control - it may well happen that when one falls from a Brahma Realm and is reborn in a lower - one forgets about one's past life and one's bad karma having matured - one's intention is no longer pure (Moreover, the circumstances one is reborn in may be exceptionally disagreeable/unfavorable for treading the Path of Purity - depending on one's karma of course). I think the following story should make this point clear.</p>

<blockquote>
  <p><strong>IN BRAHMA LAND HE SHINES BRIGHT; IN PIG'S PEN, TOO, HE FINDS DELIGHT</strong></p>
  
  <p>At one time, the Blessed One went into Rãjagiri for almsround. On
  seeing a young female pig, the Blessed One smiled. Noticing the white
  radiation which shone forth from the teeth of the Buddha, the
  Venerable Ànandã knew that the Buddha was smiling. Accordingly, he
  asked: "What has caused, Sire, to smile?"</p>
  
  <p>The Blessed One pointed out the young female pig to Ànandã and said,
  "See that young female pig? She was a young woman in human existence
  during the dispensation of Kakusanda Buddha. When she died, she was
  reborn a hen in the neighbourhood of a monastic feeding hall. The
  small hen fell victim to an eagle. But earlier she happened to have
  heard the recitation by a yogi Buddhist monk of a meditation subject
  which aroused in her wholesome thoughts. By virtue of these merits,
  the small hen was reborn as a princess named Ubbari in a royal family.
  The princess Ubbari later left the household life and became a
  wandering mendicant. Residing in the mendicants' residence she
  happened one day to gaze at the maggots in the latrine. The worms
  served as an object for meditation (contemplation of ugliness of
  worm-infested corpse or contemplation of a white object) by which she
  attained the first jhãna. When she passed away, she was reborn a
  Brahma in the first jhãnic Brahma world. On expiry from the Brahma
  world, she became the daughter of a rich man in the human world which
  she left again only to be born a pig now. I saw all these events which
  made me smile."</p>
  
  <p>On hearing this story of repeated births in various existences,
  Venerable Ànandã and other monks became greatly alarmed and agitated
  with religious emotion. The Blessed One stopped going on alms-round
  and while still standing on the roadway, started teaching the dhamma
  in six verses, the first one of which stated:</p>

<pre><code>Yathãpi móle anupaddove dalhe,
chinnopi rukho punareva róhati
evaõpi tanhã nusaye anuhate
nibbattati dukkhamidaõ punappunam
</code></pre>
  
  <p>'If the main roots of a tree remain undamaged and in good condition,
  even when the upper branches are cut off that tree will grow again
  developing new buds and shoots. Likewise, if there remains defilements
  (lying dormant) which are not yet eradicated by ariya magga, this
  suffering of rebirth will arise time and again successively.'</p>
  
  <p>What is conveyed by this verse is this: 'During her existence as
  princess Ubbari, she renounced the world to become a wanderer. By
  practising meditation, she attained the first jhãna which could dispel
  or put away by vikkhambhana pahãna (elimination by discarding) only
  the defilements of pariyutthana class, i.e. craving for sensual
  pleasure which appears as sensuous thoughts at the mind's door. By
  means of vikkhambhana pahãna, jhãna can put away the defilements only
  to a certain distance for a certain period of time. Thus, she was able
  to dispel the craving for sensual pleasure when she attained the first
  jhãna and later in the Brahma world. But when she was born again in
  the human world as the daughter of a wealthy man, the craving for
  sensual pleasure reappeared because it had not been rooted out by the
  ariya magga. The bhava tanhã (craving for existence), of course,
  persisted even when she had attained the jhãna. Because the latent
  defilements had not been completely uprooted, she had to descend from
  the Brahma world, through the human world, into a pig's existence. So
  long as the craving persists, repeated rebirths will take place in
  this way in various existences.'</p>
  
  <p>In reference to this story of descent from the Brahma world to a pig's
  existence, ancient Sayadaws had left an aphorism, 'In Brahma land, she
  shines bright; in pig's pen, too, she finds delight'. But it is not
  possible to be reborn as a pig straight from the Brahma world, nor as
  any other animal nor in the realms of petas (starving ghosts) nor in
  the states of misery. By virtue of the upacãra bhãvanã, the access
  meditation, proximate to the jhãna previously attained, rebirth can
  take place only as a human being or in the celestial abode. The young
  female pig of the above story also passed through human life where she
  was born as the daughter of a wealthy man. It is quite possible that
  she landed in a pig's existence after being the daughter of a wealthy
  man because of the bad kamma she had committed then, in being haughty
  and insolent to those she should have shown respect.</p>
  
  <p>When the young female pig died, she was reborn in a royal family of
  Suvannabhumi, which is generally taken to be the country of Thaton.
  Some scholars, however, take Suvannabhumi to be the Sumatra island,
  relying on the bronze inscriptions made by the King Devapala about
  1500 Buddhist era.</p>
  
  <p>From being a princess of Suvannabhumi, she passed over to Varanasi,
  India, as a woman. She then became a woman in Varãnasi, in south-east
  of Bombay. From there, she was reborn the daughter of a horse-merchant
  in the seaport town of Supparaka, north-west of Bombay. Next, she
  became the daughter of a shipowner at the port of Kavira in the
  south-easternmost part of the Indian peninsular. This is the coastal
  district inhabited by the Tamil people, formerly called Damila. After
  that life, she was reborn in the family of a government official at
  Anuradha or present day Sri Lanka. Her next life was as a daughter of
  a rich man, named Sumana from Bhokkanta, a village south of Anuradha.
  She took the same name as her father, Sumana. Later her father left
  that village and settled down in the Mahãmuni village of the Dighavapi
  District. One day, a minister of the king Dutthagãmini, named
  Lakundala Atimbara, happened to visit the Mahamuni village on a
  certain business. Upon seeing the young lady Sumana, he fell madly in
  love with her. He married her with great pomp and ceremony and carried
  her off to his village, Mahãpunna.</p>
  
  <p>The Venerable Mahã Anuruddha, who resided at the monastery of
  Taungsun, happened to visit her village for alms-round. While waiting
  for offer of almsfood at the gate of Sumana's house, he saw Sumana and
  said to his monk followers: "Bhikkhus, how wonderful, what a marvel!
  The young female pig of the Blessed One's time is now the wife of the
  minister Lakundaka Atimbara."</p>
  
  <p>On hearing this exclamation, Sumana, the wife of the minister,
  developed jatissara ñãna (knowledge of previous existences). With the
  help of this faculty, she recalled to her mind the previous existences
  she had passed through. In consequence, she became agitated with fear
  at the prospect of repeated births in the cycle of existences. Asking
  permission from her minister husband, she went to a bhikkhuni
  monastery and got herself ordained. After ordination, she listened to
  the discourse on Satipaööhãna Sutta at Tissa Mahã Vihãra monastery.
  Practising mindfulness meditation in accordance with the sutta, she
  became a sotapanna, well-established as a stream-winner in the first
  stage of the Path and Fruition. Then, when king Dutthagamini came on
  the throne, she went back to her native village, Bhokkanta, where at
  the Kalla Mahã Vihãra monastery she heard the discourse on Asivisopana
  Sutta which enabled her to attain the fourth stage of the Fruition and
  became an Arahat, completely free from influxes, passions.</p>
  
  <p>Going over the thirteen existences of Sumana thoughtfully and
  mindfully, one could get aroused with religious emotion. When, as the
  young woman at the time of the Kakusanda Buddha died, she left behind
  her family, possessions and her own physical body. The bereft family
  and friends would have grieved over her death. She became a hen. What
  a frightful thought, a human being to be reborn a hen! That hen would
  have a family and friends, too. She met with a terrible death, from
  decapitation, when an eagle seized her and struck her fiercely with
  its beak. There is consolation, however, that she was reborn a
  princess for the merit accrued from having heard a discourse on
  meditation. The hen would not, of course, know anything of the dhamma,
  but as she had given devout attention to the discourse, certain merit
  would have accrued to her for which she was reborn a princess.
  Listening to a dhamma discourse is thus very beneficial and fruitful.</p>
  
  <p>It is a matter for gratification that she became a Brahma after being
  a princess by virtue of her jhãnic attainments. It is gratifying too
  that from the Brahma world she was reborn in the human world into a
  wealthy family. But it is very distressing to know that she left
  behind her family, friends and possessions reluctantly to be reborn a
  female pig. It is really frightful to think of descending to human
  plane from the Brahma world and to sink further still into animal
  kingdom as a pig. This should be enough to excite alarm and religious
  emotion because so long as the noble ariya magga has not been
  established, anyone is liable to find himself landed in lowly states
  of existence. It was with the intention of arousing religious emotions
  and exhorting the bhikkhus to take to dhamma in all earnestness that
  the Blessed One had told them the account of the female hen's
  succession of existences.</p>
  
  <p>How the young female pig met her death was not mentioned in the texts,
  but it could be presumed that she was slaughtered by her breeder as in
  modern times. The young female pig must have had a family and friends
  which she left behind, causing grief to them. It was comforting that
  she was reborn afterwards as a human being in six places from
  Suvannabhómi to Anurãdha. But in each of these existences, every time
  she departed from one life there must have been considerable suffering
  from sorrow, lamentation and grief for her and her dear ones. That she
  finally became Bhikkhuni Sumana Theri is the most heartening part of
  the story.</p>
  
  <p>The cause of the succession of her existences departing from one life
  to be reborn in another is tanhã or samudaya saccã, the Truth of the
  Origin of Suffering. Other people who are not yet rid of tanhã will
  likewise go through the cycle of rebirths, dying from one life to be
  reborn in another. It is extremely important, therefore, to get
  established in the practice of the Noble Ariyan Path in order to
  eradicate tanhã, otherwise called the Truth of the Origin of
  Suffering. Sumana Theri first heard the discourse on Satipatthãna
  Sutta. Then she practised mindfulness in accordance with the
  Satipatthãna method which helped her attain the status of sotapanna
  (the stream-winner). Then, hearing the Asivisopana Sutta, she devoted
  herself more ardently to the practice and attained Arahatta Fruition
  to become a female Arahat. Tanhã, otherwise samudaya, was completely
  eradicated from her. Therefore, there would be no more rebirth for her
  and she would be enjoying peace after her parinibbana.</p>
  
  <p>Sumana Theri, therefore, declared to her colleagues that she would
  fully pass away (parinibbhuto) after the ayusaïkhãra, the vital
  principle for her present existence had become exhausted. Thereupon,
  her colleagues, bhikkhus and bhikkhunis requested of her the story of
  her existences. "I was a human woman at the time of the Kakusanda
  Buddha. When I died from there, I became a hen. I was killed by an
  eagle which broke off my head and devoured me. Then I became a
  princess in the human world . . ." she continued to recount her past
  existences till the time of her final existence at Bhokkanta village.
  She concluded, "Thus have I passed through thirteen existences
  encountering the ups and downs, vicissitudes of life in each
  existence. In this last existence, being wearied of the cycle of
  rebirths, I have become an ordained bhikkhuni and finally attained
  Arahatship. I urge all of you, my righteous bhikkhus and bhikkhunis,
  to put forth your endeavour mindfully to become fully accomplished in
  sila, samãdhi and paññã." Then she passed away, causing religious
  agitation in the minds of her audience, consisting of men, women,
  bhikkhus and bhikkhunis. This story of the young female pig is fully
  described in the commentary to the Dhammapada.</p>
</blockquote>

<p>And of course - the important thing to realize is that the Brahmas Realms or even Bodhisattas are still not completely free from suffering - So, it is important ask oneself - Why would one wish to be content with a lesser amount of suffering - when the complete cessation of suffering has been declared to the world by the Tathagata ?</p>

<p>You can read in greater detail about rebirth and dependent-origination here :
<a href="http://www.buddhanet.net/wheeld05.htm" rel="nofollow">http://www.buddhanet.net/wheeld05.htm</a></p>

<p><strong>This is how the Buddha compares rebirth in the Brahma Realm with Nibbana :</strong></p>

<blockquote>
  <p>Sariputta : "What do you think, Dhanañjanin? Which is better: hell or the animal
  womb?"</p>
  
  <p>"The animal womb is better than hell, Master Sariputta."</p>
  
  <p>"... Which is better: the animal womb or the realm of the hungry
  shades?"</p>
  
  <p>"... the realm of the hungry shades..."</p>
  
  <p>"... the realm of the hungry shades or human beings?"</p>
  
  <p>"... human beings..."</p>
  
  <p>"...human beings or the Four Great King devas?"</p>
  
  <p>"...the Four Great King devas..."</p>
  
  <p>"...the Four Great King devas or the devas of the Thirty-three?"</p>
  
  <p>"...the devas of the Thirty-three..."</p>
  
  <p>"...the devas of the Thirty-three or the Yama devas?"</p>
  
  <p>"...the Yama devas..."</p>
  
  <p>"...the Yama devas or the Tusita devas?"</p>
  
  <p>"...the Tusita devas..."</p>
  
  <p>"...the Tusita devas or the Nimmanarati devas?"</p>
  
  <p>"...the Nimmanarati devas..."</p>
  
  <p>"...the Nimmanarati devas or the Paranimmitavasavatti devas?"</p>
  
  <p>"...the Paranimmitavasavatti devas..."</p>
  
  <p>"...the Paranimmitavasavatti devas or the Brahma world?"</p>
  
  <p>"Did Master Sariputta say, 'Brahma world'? Did Master Sariputta say,
  'Brahma world'?"</p>
  
  <p>Then the thought occurred to Ven. Sariputta, "These brahmans are set
  on the Brahma world. What if I were to teach Dhanañjanin the brahman
  the path to union with the Brahmas?"</p>
  
  <p>[So he said:] "Dhanañjanin, I will teach you the path to union with
  the Brahmas. Listen and pay careful attention to that. I will speak."</p>
  
  <p>"As you say, master," Dhanañjanin the brahman responded to Ven.
  Sariputta.</p>
  
  <p>Ven. Sariputta said: "And what is the path to union with the Brahmas?
  There is the case where a monk keeps pervading the first direction
  [the east] with an awareness imbued with good will, likewise the
  second, likewise the third, likewise the fourth. Thus above, below, &amp;
  all around, everywhere, in its entirety, he keeps pervading the
  all-encompassing cosmos with an awareness imbued with good will —
  abundant, expansive, immeasurable, without hostility, without ill
  will. He keeps pervading the first direction with an awareness imbued
  with compassion ... appreciation ... equanimity, likewise the second,
  likewise the third, likewise the fourth. Thus above, below, &amp; all
  around, everywhere, in its entirety, he keeps pervading the
  all-encompassing cosmos with an awareness imbued with equanimity —
  abundant, expansive, immeasurable, without hostility, without ill
  will. This, Dhanañjanin, is the path to union with the Brahmas."</p>
  
  <p>"In that case, Master Sariputta, pay homage to the Blessed One's feet
  with your head in my name and say 'Lord, Dhanañjanin the brahman is
  diseased, in pain, severely ill. He pays homage with his head to the
  Blessed One's feet.'"</p>
  
  <p>So Ven. Sariputta — when there was still more to be done, having
  established Dhanañjanin the brahman in the inferior Brahma world —
  got up from his seat and left. Then, not long after Ven. Sariputta's
  departure, Dhanañjanin the brahman died and reappeared in the Brahma
  world.</p>
  
  <p>And the Blessed One said to the monks, "Monks, Sariputta — when there
  was still more to be done, having established Dhanañjanin the brahman
  in the inferior Brahma world — has gotten up from his seat and left."</p>
  
  <p>Then Ven. Sariputta went to the Blessed One and, on arrival, having
  bowed down to him, sat to one side. As he was sitting there he said to
  the Blessed One, "Lord, Dhanañjanin the brahman is diseased, in pain,
  severely ill. He pays homage with his head to the Blessed One's feet."</p>
  
  <p>"But why, Sariputta — when there was still more to be done, having
  established Dhanañjanin the brahman in the inferior Brahma world — did
  you get up from your seat and leave?"</p>
  
  <p>"The thought occurred to me, lord, 'These brahmans are set on the
  Brahma worlds. What if I were to teach Dhanañjanin the brahman the
  path to union with the Brahmas?'"</p>
  
  <p>"Sariputta, Dhanañjanin the brahman has died and reappeared in the
  Brahma world."</p>
  
  <p><em>Dhanañjāni Sutta (MN 97)</em> </p>
</blockquote>
 -1: <p><em>"<strong>[...] This also means that this person loses his personhood (although this personhood is impermanent and is part of dukkha).</em>"</strong></p>

<p>I wouldn't say "loses". It may be worth reminding that Nirvana should not be considered annihilation. Complementing:</p>

<blockquote>
  <p>Bhikkhus, it is impossible that a bhikkhu who considers nibbāna to be suffering will possess a conviction in conformity [with the teaching]. [...] [But] it is possible that a bhikkhu who considers nibbāna to be hapiness will possess a conviction in conformity [with the teaching].</p>
  
  <p>-- <em>Nibbāna</em> [Bodhi Trans.], AN 6:101</p>
</blockquote>

<p><em>"<strong>On the other hand, by achieving the first four Jhanas, a person could be reborn in the Brahma realms, which I understand to be the best beings in the universe, besides the Bodhisattvas.</strong>"</em></p>

<p>Personal preferences aside, if we are talking about <em>happiness</em>, Nibbāna is declared to be supreme. A happiness and security from suffering unknown to a Brahma or Bodhisattva.</p>

<p>Also, perhaps is not so surprising the idea of devas of superior realms desiring to be born as humans:</p>

<blockquote>
  <p>"It's a gain for you, monks, a great gain, that you've gained the opportunity to live the holy life. I have seen a heaven named 'Six Spheres of Contact.' Whatever form one sees there with the eye is desirable, never undesirable; pleasing, never displeasing; agreeable, never disagreeable. Whatever sound one hears there with the ear... Whatever aroma one smells there with the nose... Whatever flavor one tastes there with the tongue... Whatever tactile sensation one touches there with the body... Whatever idea one cognizes there with the intellect is desirable, never undesirable; pleasing, never displeasing; agreeable, never disagreeable.</p>
  
  <p>-- <em>Khana Sutta</em>, <a href="http://www.accesstoinsight.org/tipitaka/sn/sn35/sn35.135.than.html" rel="nofollow">SN 35.135</a></p>
</blockquote>

<p><em>"<strong>[...] but one could keep trying over and over to be reborn again and again in the Brahma realms.</em>"</strong></p>

<p>...and, while trying, out of inattention or forgetfulness or simply <em>ignorance</em>, one may do something foolish -- because that's what we do as ignorants. Foolish enough to open one's mind to darker unwholesome states, perhaps in a chain reaction, and end up in a worse destination (though reappearing as a human during a time with no dhamma, and no condition to develop oneself to become a Buddha might be bad enough). Perhaps you were Brahma before, and now here you are, among humans (again?). I guess, as long as one thinks this endeavor is worth...</p>

<p><em>"<strong>The question is, why should sentient beings choose to end their personhood permanently, rather than trying to be reborn again and again as the best person possible?</strong>"</em></p>

<p>One way of answering is to ask "What's to end?".</p>

<p>Here is an appeal from the Buddha himself as to why one should reach Nirvana:</p>

<blockquote>
  <p>"Bhikkhus, this samsāra is without discoverable beginning. A first point is not discerned of beings roaming and wandering on hindered by ignorance and fettered by craving. What do you think, bhikkhus, which is more: the stream of tears that you have shed as you roamed and wandered on through this long course, weeping and wailing because of being united with the disagreeable and separated from the agreeable -- this or the water in the four great oceans?"</p>
  
  <p>"[...] venerable sir, [...] this alone is more than the water in the four great oceans."</p>
  
  <p>"Good, good, bhikkhus! It is good that you understand the Dhamma taught by me in such a way. [...] For a long time, bhikkhus, you have experienced the death of a father ... the death of a brother ... the death of a sister ... the death of a daughter ... the loss of relatives ... the loss of wealth ... the loss through illness [...]. For what reason? Because, bhikkhus, this samsāra is without discoverable beginning ... It is enough to experience revulsion towards all formations, enough to become dispassionate towards them, enough to be liberated from them."</p>
  
  <p>-- <em>Tears</em> [Bodhi Trans.], <a href="http://www.accesstoinsight.org/tipitaka/sn/sn15/sn15.003.than.html" rel="nofollow">SN 15.3</a></p>
</blockquote>
