The points mentioned below would surely help you decide it by yourself.
Campus Life: (Winning Institution - NIT Trichy)
Thus, the campus life at NIT Trichy is better than IIIT Allahabad.
Coding Culture: (Winning Institution - IIIT Allahabad)
A higher rate of students at NIT Trichy belongs to the core branch whereas, at IIIT Allahabad, the majority of the students are coders. Therefore, the coding culture at IIIT Allahabad is better than NIT Trichy.
Higher Studies: (Winning Institution - IIIT Allahabad)
IIIT Allahabad is a much better option if you wish to do MS from foreign universities.
Placement: (NITT~IIIT Allahabad)
When it comes to placement, there is not much difference in both institutions.
So, go through these points and choose the institute according to your convenience.