First thing I am not able to understand is why your friend gave JEE again even after getting a decent branch in such a good NIT.
Don’t even think of taking IIT Patna over NIT Trichy that too after 1 year. If I have been there, and even if I had both choices at first attempt only (No year Lag) , I would have preferred NIT Trichy.
NIT Trichy is well established college whereas IIT Patna is still struggling for good faculty and Infrastructure.
Please don’t go for an IIT tag, it’s not that much worthy.