Hii there,

Dear candidate, below I'm providing the link of comparing both the colleges, please do find the difference

https://www.careers360.com/compare-colleges

I would suggest you to choose the college based on your rank, the college which has lower closing rank are more beneficial to you. College placements of IIID is more than that of NIT patna, but yes the fees is also higher for IIID. IIID is more top rated college by NIRF, and also both are public owned.

Good luck!!