I think if you dont have any issue giving up the IIT Tag and at the same time interested in pursuing studies in Computer Science, Mathematics and subjects like Machine Learning and Artificial Intelligence, you might just prefer NIT R over IIT BBSR. NIT Rourkela is one of the best technical institutes in Eastern India, when it comes to Computer Science, next to IIT Kharagpur and at par with institutes like Jadavpur University and newer IITs at Patna and Bhubaneshwar. The institute has good infrastructure, faculty, research facilties and an excellent employer outlook with nearly 100% placements for CSE.

However, if you want to study Core Engineering like Mechanical and also have some heart for the IIT Tag, IIT Bhubaneshwar is a good place to be. Mechanical after CSE and Electrical has one of the best placements in campus and also has good infrastructure in development. Most of the Top Companies like Tata Motors, Tata Steel, Jindal Stainless, Vedanta, Reliance, Maruti Suzuki, Tata Projects, L&T, IOCL, GE visit regularly during campus placements. However you might miss a complete feel of campus life and peer environment as well as certain facilities, at par with Older IITs and Top NITs. Choose wisely.