BITS Pilani is anyday better than IIT Patna. If fees is not an issue, please go with the former. But if you are getting lower branches in BITS and top stream in IIT Patna then only go with the latter.
Placement wise: At par with top 5 IITs ( Software, Core and Non-core).
Peer group : Definitely at par with top 5 IITs ( No reservation ).
Alumni : This is really strong here. You will find BITS alumni in every sphere ( Top foreign universities, IIM ABC, Civil services etc. ).
Entrepreneurship : This is 2nd best after IIT Delhi.
College life : This is would be also great because of its massive infrastructure and zero attendance policy. But, mind you it’s in a small city. Life outside the campus won’t be good.
So if you are getting similar branches in both the institutes and fees is not an issue ( the difference in fees is around 8 lakhs ), please go with BITS Pilani anyday.
Note: IIT brand is diluting( There are total 23 IITs. Recruiters and every aware person understand the brand value of each IIT and other institutions. So, don’t get swayed away by the IIT tag. IIT Dharwad is not same as IIT Delhi or IIIT Ranchi is not same as IIIT Hyderabad