For the first year, all students study the same subjects. Not much of laboratory work too. So it is only a matter of professors being asked to take up some more classes.
After the first year, you would be in your own environment. Most likely half built and professors would avoid shuttling between their parent IIT and the new ones. So the least influential would be asked to do the job and most likely they would be junior professors or new ones recruited.
I am not saying that new IITs are bad. But when comparing BITS Pilani and new IITs, why gamble ?
Just take BITS Pilani and be happy. Or else jump into the abyss not konwing where you are going to land.
Happy Mechanical Eng. buddy