Let me put it in simple words.
1. As stated in a reply, your budget really matters. If you are on a tight budget you are better off training in India from a good school than going abroad to the US and struggling with finances.
2. Pilots will suggest a lot of things. A US license will give you no edge when it comes to applying jobs in India since the Indian CAA will ask you to convert it. So you are as good as anyone who has flown in India for half the cost.
3. As 350xwb suggested, the Indian CAA doesn't really like the FAA. Same as other South Asian CAA bodies. Lots of red tapes in converting your license to an Indian one.
4. You can not fly in the US after finishing your training unless you have a green card. That's a mandatory prerequisite these days.
My suggestion, fly in India, get into an Indian airline and build your career.