Hey there,

Not looking at the issue with course point of view, each of the college has it's own reputation, pros and cons. If you choose to study a core branch, IITs are preferable because most of the core companies recruit students there and all the recruitments would likely get filled by IITians, NITians. The value of the student who has done graduation in an IIT would be high. The fee structure is much student friendly in IITs/government colleges. IITs have high quality of competition than BITS. But, BITS follow zero attendance policy which would be easy for passion oriented students who are willing to work for startups, etc. although IIT has few courses which doesn't require students to satisfy attendance criteria. Nevertheless, each of the colleges have breathtaking campuses, good clubs, great facilities. 

Hope this helped. 

BITS Pilani is known for its computer-oriented courses rather than core ones. IIT Madras has a good faculty and infrastructure for metallurgical students. However, you should consider your own interests and inclinations since these two are very different courses. Find out which subject is more suitable for you rather than the college. Best of Luck.