Your medical degree will be recognized in the US (as noted above, AIIMS has a lot of graduates working in the US).
If you wish to be a surgeon in the US however, do not do surgical training in India. Currently, we are moving toward more required certification by the American Board of Surgery. You cannot be Board Certified if you have trained outside of the US. More recently, the American Board of Surgery (ABS) decided to allow up to 2 years credit for any training done abroad; however, you have to be in a US surgical training program to apply for and receive that credit. There are rare exceptions in which someone who has completed their training abroad is allowed to work in the US as a surgeon; in most cases you will be expected to repeat your entire training curriculum.
Therefore, your first task is to decide where you want to LIVE and PRACTICE. If it is in the US, then review the steps for getting into US training at
www.ecfmg.org,
www.usmle.org and
www.nrmp.org
Surgical training can be somewhat difficult for an FMG to get into in the US, but not impossible.
Your income and lifestyle in the US is not based on where you trained; as I noted above, for all intents and purposes, your surgical training abroad will not be recognized and you need to do that training here if your intent is to work in the US. I cannot speak about Canada or other countries. The US is an insurance based company and surgical work is based on insurance reimbursement for certain procedure codes; you do not make more if you go to a more prestigious training program. Everyone makes the same (with some regional variation).
best of luck to you...