Hey Aryan,
Great questions and something I get a lot from Indian Applicants!
1) There is no program that is better especially when you don't have on campus placements abroad but If you are targeting I would suggest MSBA more than an MiM. Simply because MiM is still a bit new in the US and there aren't a lot of options there apart from 3-4 top colleges.
2) MSBA can surely get you Strategy roles, Consulting roles but you really need to build your profile accordingly while being in the college. In fact you can do some research on LinkedIn, I am sure you will be able to find a couple of people in these roles Post MSBA.
Almost all the top Colleges have an MSBA in USA. name might be a bit different but the course is the same. For example in Duke its called MQM. Recently NYU also launched, Management and Analytics, UT Austin has a decent program, USC Marshall is very good.
Would love to chat with you if you have any further questions!
Kevin Rajan Singh
Founder, Al-Connect