Does a PhD from US carry *more academic value* as compared to one in India even if the research skill set developed is same? I am currently an Indian undergrad in physics in my final year. My area of interest has very strong groups at two institutes in my country, and I have both the options before me.  But the story does not end here.
I have a friend who is a graduate student at an Ivy college in the US who has recently suggested that it would be much better to get into a PhD program in the US, because according to them

even if the knowledge and research skill set developed could easily be the same between X,Y institutes and a top school in the US, to apply for academic positions in India, a PhD from the US has more value.

But many people I have talked to have told me that a PhD is not really about QS rankings or a country. It is about the quality of the work that you have done as well as how strong the corresponding research community is at your institute.
These two views are opposites of each other, and I am not sure how to proceed from here. I personally prefer to stay in my own country due to a number of reasons.
Any help is appreciated.
While I was an Indian undergrad in mathematics, I was told similar things by my friends who were doing, or planning to do, their graduation at universities abroad. Specifically, they told me that:

The top universities abroad are better than the top universities in India for graduate education.
Even if I were to be admitted to a good university abroad whose graduate program is comparable to that of an Indian university, the university abroad will be more beneficial for two reasons.

Experiencing a different culture will broaden my perspective significantly, and help in my growth by opening my eyes to more possibilities.
I can build a larger pool of contacts at a university abroad than at an Indian university, and doing so is very important to gain further opportunities in academia.
Somewhat connected to the above points, one can expect more invited talks (and also given by more top researchers) at universities abroad than at Indian universities, and it not only stimulates ones growth by being exposed to diverse topics through such talks, but also gives more opportunities to build contacts with top researchers.



Of course, there is an underlying assumption in all of the above that it is meaningful to speak of the characteristics of &quot;the average Indian university&quot; and &quot;the average university abroad&quot;. I preferred to read their advice as saying, &quot;If you compare the opportunities at a university abroad versus an Indian university, assuming that you want to get into those universities and are fairly confident of being able to do so, then it's more likely than not that the university abroad offers the above advantages over the Indian university.&quot; Read like this, I think my friends offered a fair assessment of the advantages.
I still chose to pursue my graduate education in India, for the following reasons:

I anticipated that my graduate education would be a difficult time for me, and I would need the support of my family to help me through it. If I were to be abroad, I would have a much more difficult time coping with the stress than if I were in India itself. There seemed to be little point in trading my mental health for more contacts and comparatively better future opportunities; after all, it's not like a graduate education in India dooms my future in academia.
And indeed, my graduate education started off on quite a rocky note, and the support I have received from my family has truly been invaluable.

I anticipated that choosing a guide would not be an easy task. Not everyone who is a good researcher is also a good guide. Not everyone who can be a good guide is specifically a good fit for me. In short, I felt that gambling on my chances of finding the right fit for me at a university abroad is riskier than doing the same at an Indian university: the stakes are lower, the sunk cost (in case I fail to find a good match for me) is also lower, and hence my ability to try again at another institute (in case of failure at one institute) is also higher.
As it happens, I nearly failed my qualifying exams after I secured admission at an Indian university, and nearly signed up with a guide with whom I had spectacular incompatibility issues. Things have sorted themselves out now and I am happy to say that my work is progressing well, at last.


Furthermore, among my friends who pursued their graduate education abroad,  some did struggle with their mental health and returned to India to get support from their family, some did fail to find a suitable guide and were forced to return home and start over in India, and some who pursued their graduate education in India also failed and started over in India. There are also those who succeeded, of course, but I just want to emphasise that it's not such a rare event to face these kind of difficulties that they can be easily neglected from the equation.
In your case, the final decision lies with you, of course. You need to decide how much weight you give to each relevant aspect. For me, the balance weighed in favour of staying back in India. For my friends who were more ambitious and also mentally stronger, the balance fell the other way. Neither path is absolutely right or wrong: you need to measure what is right for you, as best as you can perceive. Good luck!