Some of my friends studied at MNNIT, so I might be able to answer your question. It is suggested that you choose Mechanical at MNNIT Allahabad rather than Civil at NIT Trichy.

Your branch of choice is more important than your college preference. In terms of opportunities, Mechanical Engineering has a slight advantage over Civil Engineering

Mechanical at MNNIT Allahabad has a consistent placement record. Mechanical students receive more job offers than Civil Engineering graduates. PSUs often choose Mechanical Engineering graduates.

Finally, everything depends on your interest and choice. So think wisely and then make any decision, because this will be the building blocks of your career.