Q:

What is the point of experience?

I've just started playing Final Fantasy 8 for the first time, and I've come to understand that monsters level up with you. So from what I can find, the game doesn't get easier with grinding, with only a few exceptions (monsters that have level caps, so I've read). 
So then what is the point of character level/experience? I understand that GFs level up, but it seems to be a wash when it comes to characters.
I'm sure I'm not the first person to ask this, but I can't seem to find a straight answer anywhere; just guides on how to best perform leveling .. which seems pointless.
At least in other FFs you could grind if you were having a difficult time with a particular enemy or boss, or you wanted to easily farm some desired item. That back-up strategy seems lost in FF8.

A:

It raises stats, though Junctions raise stats far more effectively for the most part. The main purpose of leveling is to raise enemy's tiers--higher tiers (the max tier is actually very low, around level 40 I think?) drop better items. Higher tier enemies also use more dangerous spells or attack patterns however.
For instance, Elnoyle will drop Moon Stones at low tiers, but Energy Crystals (useful for gaining Ultima) at a high tier.
Also, certain encounters have fixed levels. But generally speaking, leveling will actually make enemies harder, though they will drop better item rewards. Much progress in FF8, unlike most other FF games, is related to items directly or indirectly, so they shouldn't be ignored. By fighting higher tier enemies you can more easily synthesize high level magics, weapons or GF ability items. 
Grinding in FF8 is rarely direct, aside from AP. (It's also rarely necessary) Grinding to level 100 may seem pointless, but grinding Energy Crystals will give you plenty of Ultima which is both a very useful spell, and the best stat raising junction for several stats.
You can also grind if you WANT to make the game harder. Personally the first thing I do when possible is head straight to the Island Closest to Hell and get to level 100 (which due to FF8's leveling system and the level 100 enemies, does not take long).

A:

There are two main benefits to leveling up:
1) Getting AP points for your GF's. Without your GFs getting stronger, and learning new abilities (especially item-refining abilities), it's hard to beat many bosses. Therefore, the main point in 'grinding' in FF8 is to level up your GFs.
2) Even though enemies level up with you, if you level up with some GF stat-boosting skills, such as Strength-Up from Ifrit, you will get extra stats (effectively putting you ahead of the enemies).
@Jonathan Drapeau - Most bosses do, in fact, also level up with you.
In conclusion, there isn't much benefit to grinding in Final Fantasy 8 (unlike other Final Fantasy games - excluding Tactics). In fact, if you use GameShark and skip right to the end, you can hypothetically beat the final boss at a very low level because it'll be weak.
As for the best strategy? Find enemies that yield high AP and low EXP, get stat-boosting skills with your GFs ASAP. Once you have a good amount of stat-boosting skills, then level up your characters!

