Hello.

TIFR only works on fundamental research so you'd be doing a lot of research on basic aspects of everything, while IIT would train you in applied research where you apply already known concepts to your research. It's upon you and your interest like whether you'd like to work on fundamentals or apply your fundamentals on some other research. Talking about the placements, both of these institutes are two of the best that anyone would aim for. They have a pretty good recognition in India as well as abroad and would help you fetch a very good career. 

I hope this answer would have cleared your doubts. If you still have any more doubts, feel free to ask.

Thank you, all the very best.