It doesn't differ much in these two countries. Struggle of PhD depends upon supervisor and research grants and facilities.
But talking in deep which sometime matters a lot like:
1) Freedom of working culture and timing, you get more in India. but at the same time in US you get more structured and disciplined time-table for work.
P.S.: This is more of general outcome, mostly depend upon supervisor.
2) Funding: definitely you get more in US than India. You get various fellowship.
3) If you are open to work worldwide in future, you should definitely try PhD in abroad (USA), it gives more working scope and opportunities.
I am saying all these from my experience as I am doing PhD from India (IITM, best engineering institution in India ) and also from Michigan State University, USA.