Since you did not specify the criteria, I will be comparing the aforementioned institutes on the basis of 2 main criteria placements and campus life.
NIT Patna has a well-maintained campus and enjoys a good reputation being one of the oldest engineering colleges in India. However, the academic rigor is poor and the professors aren't interested in teaching. Moreover, it suffers a lot because of its location in Bihar one of the most underdeveloped cities in India.
NIT Puducherry has the best location among these institutes. It is located near the sea beach and students get to enjoy the picturesque view of The Bay of Bengal.
NIT Andhra Pradesh should be your last priority because it has many major cons like lack of campus, ragging, and poor placement scenario.