Hello,
The question is not complete. What course you are looking for? Which branch? What are your choosing criteria? Are you looking for PG courses or UG? A lot of these come into picture when you compare between these two IITs.
Talking in general, even though the recent NIRF rankings suggest IIT-BBS to be in a better position than that of IIT Patna, IIT Patna has always been ahead in terms of academics, placements, and research. It is running in its permanent campus since 2015 and has almost all the facilities within the campus itself. It is well connected by rail and by air to all the major cities in India. Course curriculum, be in UG or PG, are up to a high standard that incorporate state-of-the-art innovations and research domain. Most of the UG students get high end placements during on campus placement drives. Internships are an integral part of the curriculum.
Apart from academics, students also engage themselves in multiple extra-curricular activities including participating in various technical events, organizing on campus technical programs, cultural events etc. IIT Patna also has entrepreneurship-club and an incubation center to encourage students to take entrepreneurship activities. All in all, IIT Patna is an excellent institute to be in and enjoy learning.