Chemical Engineering

NIT TRICHY is better than ANNA UNIVERSITY.
I would say both are very good in their own rights. CEG takes in a lot of candidates mainly based on TN state board marks. So the quality may be a little less than students at NITT where students are taken in through JEE performance. Still you can see CEG and NITT ranked amongst the top engineering colleges in India. Considering some factors:
Placements:
NITT would win this one , as the number of candidates placed in core companies every year is much higher. This is mainly because NITs are more established all over the country than CEG. If you are looking for better chances to get placed in a core company choose NITT.
Higher Studies:
It doesnt matter which one you choose as long as you have a good GPA. Maybe CEG might edge over NITT in this one, as your chances of getting a good GPA is a lot higher due to the above mentioned reasons.
College Life:
Wherever you study it depends upon your personality and interest in things that will make your college life memorable. In CEG you have better options of exploring the city and taking a break from hostel food(decent) by visiting some excellent restaurants outside. In NITT these options are less as the college is far away from the city.
Its upto you now. Whichever college you choose, make sure to make the best out of it. Cheers!
P.S: If you really want an NIT, make sure that you get into NITT or NITK. Dropping CEG for any other NIT would be a stupid idea. Just guiding you based on my friends and my opinion.