If it’s pilani campus, then there is no comparison, pilani cs has avg placement of 27 lpa of 180 students(including dualites) while iit patna has only 21–22 lpa of 83 students, now coming to non core, pilani is much better than iit patna, in core situation is not good anywhere, but due to ps, students of mech, chem, civil, manu gets placed in exxon, mercedes Benz, jsw, bajaj, iocl, gail, skoda, tata motors, srf, hul, etc and if you compare ET sector(eee+eni core) then avg placements was 18.35 lpa, so overall placement of pilani eee is same as iit patna cs. Startup culture is also much better, peer group is also better due to no reservation, alumni network of bits pilani is one of the best in India.
So all in all pilani is much ahead of iit patna, just fees can be factor to not choose bits pilani over iit patna.
Hope it’s clear 😃
Edit: goa and hyd are also comparable or better than iit patna, but there is difference between pilani and goa/hyd(not significant one but there is)