This is a very good question. This is an exciting time for thinking about PhD opportunities in India. Things are changing (mostly for the better, but not always) and there is a good chance for people who are interested.
A PhD is not only something that you learn a specific subject matter but you learn how to think, in the process you also get the prejudices from the group that work in (hence most people after PhD will work as a Post doc in a different group (learn new prejudices:-)) ) so going to a different place is good for you to be exposed to new ideas. Also it will widen your international network (“the smart person knows everything, the wise person knows everybody”) .
Also a PhD is the result of an obsession (see my other posts on this), so you want to work with the best advisor that you can find. It is also important to go to a university that has experts in a wide range of fields. It is not just your work, but your ecosystem that matters. You will be inspired by other students and by instructors in other fields and the cross pollination of ideas is an important element. For example I was able to use ideas from Differential Geometry in metal forming because there were top people in the field who helped me learn the essence of this.
When I was an UG (that was a long time ago, Indira Gandhi was still PM!) there were not many options outside IISc for a half decent PhD. Ie the ecosystem was not well developed. Also I had the privilege to be accepted at a top school with a very well known researcher and had a nice fellowship (so not too much to worry about) so I went.
Today, the ecosystem for PhDs in India (especially IISc in STEM fields and some of the IITs in engineering) has improved a LOT. so the difference is less stark. But still, I find that (barring a few expceptions) PhD students are not encouraged to be as independent (and challenge orthodoxy) as in many western countries so this hampers innovation
Now the decision boils down to
(a) TOPIC: If a university in India has internationally reputed people in the field of interest then it is worth considering.Some of the new faculty in India who have international exposure are strongly worth considering . Dont go by # of papers published. There are a number of faculty who are “paper mills” but whose work has very little impact. Stay away from them. Some of the Senior faculty in India are too “imperial” and hierarchical for my taste (but this too is changing) but that is just my opinion.
(b) PROJECT/FUNDING: in the US atleast the funding situation is very very tight. It is more of a winner take all system (with few groups having a lot and most having to live on scraps) so if you get into a well funded group it is OK.
But the situation is much better in India, the Govt will pay you a decent (not great but pretty good) stipend so you dont have financial worries, which is a constant in the US for foreign students.
(c) BREADTH: here, most Indian universities still suffer. I would say that the breadth is reasonably good in IISc for a stem field but not so much in the other places although it is also improving. There are some excellent institutes in specific fields that are producing PhDs but they lack breadth. Without breadth, you cannot branch off into new areas of research in your career so it is vitally important.
(d) OPPORTUNITIES: If you get a PhD in india, I would recommend that you do a Post Doc outside. This will help you widen your network . Even if you plan to return to India to work (which is a good option given the enormous funding pressure for asst. profs in the US nowadays), exposure to international research will give you that independent thinking and network that you will need to succeed
(e) FAMILY: One intangible is your family situation. If you need to be close by for whatever reason, then of course the choice is made.
(e) did I mention FUNDING:-)))
Hope this helps
Arun Srinivasa, Ph.D Mechanical Engineering & Materials Science and Engineering, University of California, Berkeley (1991)
Source: Quora Digest