My uncle is a successful architect and has the experience of employing many architects. He shared his experience stating that architecture students of both BIT Mesra and NIT Trichy are Unfortunately both the institutions are engineering colleges where architecture is considered equal because both are engineering colleges with Architecture as just one of the many specializations offered by the institute. None of these institutes are specialized in this field so the students study in a more engineering-oriented ambiance. They lack the ability to think independently of constraints imposed by engineering abilities available in India. I recommend you pursue Architecture from an institution that has Architecture as its flagship course like CEPT or SPA.
Nevertheless, comparing Architecture from BIT Mesra and NIT Trichy, I will say the former has a better crowd and opportunities than the latter. Both are somewhat at similar levels and it's hard to make a direct comparison. It's that students from BITS Mesra are better exposed so they make better Architects than NIT Trichy students.
When it comes to comparison between BIT Mesra and NIT Trichy, the latter is way better than the former. Therefore, it is evident that the placement at NIT Trichy is also better than BIT Mesra.
A few points to note:
NIT Trichy would be a better choice upon BIT Mesra when it comes to architecture. But, the choice is yours.