Firstly, congratulations if you have bagged admissions from both of them. They are top-notch IITs and apart from very few there wouldn't be any significant differences in both of them. Let us get into details now, shall we?

1. Placements: Placements are almost same in both of them. So that shouldn't be the criteria of ruling anyone out.

2. Higher studies: Both the colleges have numerous MoUs with foreign universities for exchange programmes. IIT Madras has MoUs with premier institutes all over the world like UC, San Diego, University of IllInois, Rice University, Purdue University, Penn State, EPFL Switzerland, NUS Singapore, PoliMi, and many more. This is the official list: https://oir.iitm.ac.in/foreign-universities-2/

IIT Delhi, on the other hand, has 116 MoUs with some of the premiere institutes but not as much as IIT Madras. They are slightly down in this domain. This is the official list: https://home.iitd.ac.in/active-mous.php

Choose wisely!