NIT Trichy offers a great learning experience, especially in CS. EE at IIT Dhanbad and IIT Bhubaneshwar is also decent and the placements are quite good and with either of the IITs, you would get that IIT tag. So, it actually boils down to your choice between an IIT and NIT and if you want to give preference to IITs. 

The average package for EE at NIT Trichy was around 6 LPA with a 97% placement rate for EE students. On the other hand, for IIT Dhanbad, the placement percentage was 76% with the average package of around 15.5 LPA. In IIT Bhubaneshwar, the average package for 2019 was around 11 LPA and the placement rate was around 86% from EE.

Although, the tag isn’t only something one should go after. NIT Trichy’s EE is excellent and the placements are equally great. Good infrastructure, excellent teachers, and a decent learning and developing environment are what one should seek, and thereby, NIT Trichy would be an excellent choice since IIT Dhanbad and IIT Bhubaneshwar are newer IITs. NIT Trichy, Warangal, Surathkal are better than most IITs.

So, it completely comes down to your personal preference.