Choosing between NIT Agartala and a private university depends mainly on two factors, the branch you are getting at NIT and obviously your financial situation.
One needs to be financially strong if one wants to join private colleges. Moreover, not every private college is good and most of them have a poor crowd that got in by paying huge amounts. The most credible ones are BITS Pilani, BIT Meshra, VIT Vellor and VIT Bhopal. Unless you are getting these colleges, it’s better to join NIT Agartala.
If you have financial constraints or want to get the NIT tag, then NIT Agartala is a much better choice. However, the placements of some branches are really bad here so you can also upgrade your branch after your 1st year to CSE or ECE.
Ultimately, the decision will depend on your personal preferences and financial condition.