It depends on so many factors. First of all, you should know what are your priorities and future career plans.
Do you want to settle abroad ? - If yes, then go for PhD abroad. PhD study abroad will be one of the easiest ways to find some ground in finding employment and settling abroad. Not to say that finding a job after PhD will be easy but still you have other options like postdoctoral work if you want go in academics.
Do you want to settle in India? - If yes, then in academics or industry job? If academics then doing PhD abroad will give you an edge in initial stage of selection for faculty jobs. On the other hand, if you do PhD in India, then you form more contacts in India and settling in faculty jobs will be easier. For industry jobs also, contacts and references matter, so chances are better with PhD in India.
Are you confused or not sure at this stage whether you want to settle in abroad or not? - In this case, if you get PhD in reputed universities abroad with full scholarship then go for PhD abroad. You will experience global cultures and get broader outlook both in research and life experiences. You would also be able to save good amount of money during PhD abroad. If money does not matter to you so much and want to stay closer to family, then do PhD in India.
So in summary, if you definitely want to settle abroad, then go for PhD abroad. If you want to settle in India, then you can think in details about the information I have written.
Hemant Borkar, Assistant Professor at Indian Institute of Technology, Indore (2017-present
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It depends on so many factors. First of all, you should know what are your priorities and future career plans.