First of all don't choose a college just because it's famous or good in that particular subject, because at the end you have to study and survive for 3 years(since first year is common in VTU) in that subject you have selected. So I prefer u to go with the subject you like the most and which you are interested in.

If you are interested in automobiles,design field, production,field work etc I would prefer you to go with mechanical especially in MS Ramaiah since it is autonomous where you are provided with latest updates on the subjects and slightly better teaching when compared with BIT. Also the campus recruitment is good since most companies prefer autonomous colleges over VTU colleges for the campus drive.