When it comes to comparing institutions, rankings and comparisons can be found in various sources, but it's important to be unbiased in your analysis. While I cannot provide a clear answer on which institution is better, I can share my beliefs based on my experiences.
If you're considering IIIT-H, you should know that they offer courses in Computer Science and Electronics only, with Computer Science being their forte. Here's what makes IIIT-H's CS education stand out:
In terms of placements, IIIT-H, and IITs are more or less similar. In fact, CS graduates from IITs are also poached by banks and consulting firms due to their strong mathematics and quantitative analysis backgrounds. Faculty members are equally good at both places.
Unlike IIIT-H, IITs offer specializations in various engineering fields, such as Civil and Mechanical engineering. While these fields may be less appealing currently due to their reduced demand in the job market, they are still essential components of the engineering industry. Therefore, it's unfair to say that IIIT-H has grown beyond any IIT in its entirety. But as far as Computer Science is concerned, IIIT-H has carved out its own niche and excels in this field.
If you wish to have a good campus life during graduation and plan on pursuing MBA after or prepare for Civils, without any second thoughts go to IIT Chennai. But if you want to learn about CSE in the best possible way during your 4 years of engineering then IIIT-H is the right choice for you.
Placements:
Placement depends entirely on the students. However, a student with 6 CGPA at IIT Madras is more likely to get better placement than a student of IIIT Hyderabad.
Research: (Winning Institution - IIIT Hyderabad)
Due to better faculty and environment, IIIT-H produces a better quality of research than IIT Chennai and in IIIT-H you see undergrads publishing papers in top-notch conferences.
Coding Culture: (Winning Institute - IIIT Hyderabad)
In the summer of 2020, a total of 20 students from IIIT H has been selected for GSoC with 4 UG first-year students in the mix. This indicates that the coding environment in IIIT-H is at a whole new level. The best performance from any team in ACM ICPC world finals from India was from IIIT Hyd.
Finally, if you are not sure of your core and main field of interest, you should opt for IIT-M.