See both the institutes are very good. Now you have to choose among this two based on your interest in the course. If you are interested in CSE go for NIT PATNA and if you are interested in ECE then go for NIT JAMSEDHPUR.

Now if you are asking this question from a placement perspective point then I would recommend you that you should go for NIT JAMSEDHPUR. The average packages of NIT J is better than NIT P. But apart from this there are no such big difference between these two institutes.

To know more about NIT P visit the link below:

https://www.careers360.com/university/national-institute-of-technology-patna

To know more about NIT J visit the link below:

https://www.careers360.com/university/national-institute-of-technology-jamshedpur

I hope this answer helps. All the very best for your future endeavors!