(The statement that follows, is the undeniable truth.)
BITS Pilani is NOT on equal footing as the top IITs, when one considers research, teaching, or for that matter, even placements.
Any other version of the story is silly.
I did my undergrad studies at BITS, and know quite enough of the research output of the old IITs, to swear by the fact that BITS has a lot to improve, in terms of research funding and facilities.
That said, however, there are things that BITS Pilani offers its students, that lead them (self included) to believe that life elsewhere would have hardly been as much fun. The kind of people one meets and befriends at the place, and the BITSian spirit imbibed, fills one with the desire to make something of oneself—engineer or otherwise.
It’s a strange confluence of people with varied interests, beliefs and goals, all of whom seem so full of positivity, that some of that energy gets onto you and your work.