Hey there

IIT is undoubtedly take brilliant brains of India and gives you a bachelor's degree in technology if you join it. On the other hand doing engineering at Harvard and MIT will surely gives you an environment which you will not get in IITs it's a harsh fact. MIT is rank 1 engineering college and many IIT toppers move to MIT even after selection it is due to the reason that IITs take best brains but lacks in giving environment particularly for engineering that's why IITians are dropping out or changing their careers after engineering whereas MIT and Harvard are structured such that they very much focus on the research works and engineering development and thus at the end you may not end with high package like IITs but in long run you will be benefited. But foreign colleges have high fees and their entry process also checks academics and english proficiency.

Good luck