Which is better, IIT Madras mechanical or IIT BHU electronic engineering?

Both are decent options but which one is good for you depends on your interests only. In fact, whoever is going to answer this question, will be driven by his own interests and thus there is no objective answer to your question. Choose the branch that appeals to you the most, be it EE or ME.

Just bear in mind that while analyzing, placements should not be the major criteria for your judgment. You should consider versatile factors like the campus life the Institute offers, alumni network, faculty pool, etc. Don’t limit yourself to good packages and seek much more.

The best way to decipher which branch is better is to interact with seniors of both institutes belonging to the respective branches. Enquire about the opportunities, exposure, and other things that cannot be known from statistics. Only after weighing the opinions of both the parties, should you reach a conclusion that satisfies you the most.