Is it better to choose mechanical engineering at IIT Kharagpur or chemical engineering at IIT Bombay?

Getting into IIT is a big achievement only if you manage to choose the right branch for yourself.

You should analyze your ambitions and interests in a particular field and determine what you possibly imagine yourself to be doing in 5 years and then make an informed decision. Clarity of goals is extremely necessary to make this crucial decision of choosing a branch.

If you want to enter politics, then your branch hardly matters. 

If you want to become an entrepreneur try to get an idea of the type of company you want to start

Basically, the choice of the branch is strictly a personal preference and cannot be objectively decided.