I’ll try to answer it from my perspective. When you ask this question I assume that you are student who has completed 12th class and you might have seen the last year cut-offs and your rank matches with these two courses.
If these are the only two options, let me describe each with which you’ll be able to decide on your own.
Option 1:
NIT Trichy MME. Of course NIT Trichy is one of the five top NITs. So no doubt about the faculty, students, campus. I heard that the campus is wonderful and is huge (One of way of saying you can enjoy it but might be difficult for commuting). Let me talk about non-academic first. The campus has everything when it comes to sports, co-curricular activities. No second thought about them but your comparison to IITs might make my statement wrong. Talking about academics NIT Trichy maintains its standards there too. Faculty of MME is not very great at NIT Trichy. The opportunities once you graduate are not very high in India. But if you want to work overseas or study overseas then I don’t say that it is as bad as it is in India. Placements are not very great. You have to be very well acquainted with the faculty. Done there because I have only one source, not lucky to grab more.