It would be better to opt for Chemical Engineering at NIT Trichy. The institute will offer you a better faculty, upgraded infrastructure, a better peer group, and superior placements. If you are genuinely interested in chemical engineering then you have a lot of scope in NIT Trichy.
NIT Trichy is more developed as compared to the other NITs and offers a lot of exposure. Choose this branch only if you will further go for higher education in Chemical Engineering. The job opportunities right after graduation are very less and it would be difficult.
However, if you are concerned about placements, then CSE will be the suitable option as the branch has a lot of opportunities.