There is no IT branch in IIT Patna and BITS. I am assuming you are talking about CSE.
I will try to give a short and to the point comparison.
a>b: means a is better than b.
- Placement AVG:- BITS(Avg: 26–27 LPA) > IIT Patna(Don’t have data but less than BITS)
- Placement MAX :- BITS == IIT Patna
- College Life :- BITS >= IIT Patna
- Tag :- IIT Patna >= BITS
- College Fest :- BITS >> IIT Patna
- Societies :- BITS >> IIT Patna
- No. of Companies Visited For Placement:- BITS(224) >> IIT Patna(110)
- Research Practice :- IIT Patna >= BITS
- Repotation:- BITS >= IIT Patna
- Overall Development :- BITS >> IIT Patna
- College Stand in India for CSE:- BITS(usually in top 7–8 colleges) > IIT Patna(usually in top 15 colleges