IIT Madras does not offer B.Tech ECE. Instead, it offers B.Tech in Electrical Engineering. The Electrical Engineering department is one of the oldest at IITM.
Both these institutions are highly reputed in the field of engineering, and they offer equally good academics and placements. But I would recommend you opt for Electrical Engineering at IIT Madras since it has a bigger brand name and a richer legacy. Moreover, Electrical students at IITM receive even better packages as compared to ECE students at IIIT Hyderabad.
The variety of departments, faculty, and peer groups at IIT Madras can never be rightly compared with that of IIIT Hyderabad. This institute is small with a batch size of only 200-300. Even the faculty pool is small, comprising around 100 professors. There are limited branches with ECE and CS being the primary branches of the Institute. Being a non-government organization, it tends to grow faster than IITs but faces many obstacles on the way.
Despite it all, IIIT Hyderabad has a rich research culture at the UG level. Most dual degree and Honors students conduct excellent research work that makes it to some renowned conference/journal that is at tier-1 status internationally. The core courses are offered much earlier than other institutes such that students are ready to conduct research by the end of 2nd year.
The UG students are given attention in their academics and are taught to handle challenges and rigor. Many top institutes don’t pay much attention to UG students mainly because of their high strength. But IIIT Hyderabad faculty pays exceptionally high attention to them and harnesses their skills to the fullest. Even seniors contribute to making the students feel welcome in the Institute.
IIT Madras on the other hand guarantees a more diversified experience for UG students. After BTech, the IIT tag might help you avail better opportunities.
If you are ready for a focused academic experience in ECE or CS or both, then IIIT Hyderabad is the right place for you. It will provide a smooth transition from coursework in the initial 2 years with top-notch research in the last 2 years. But if you want to explore more options and want to experience diversity, then IIT Madras is the right option for you.