Anna University

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.

Hello Jayakrishnan,
From last year onwards Tamil Nadu government has disbanded any entrance exam for admissions to different engineering courses. Now, the admissions are based on the marks obtained in class 12th examination. In the initial years, there was a big restriction for outside state students from appearing for seeking admission in engineering colleges in Tamil Nadu, but with the seats not getting filled up the government has relented and now outside state students can also seek admission in engineering colleges in Tamil Nadu under quota called as quota for outside state students. TNEA ordered Tamil Nadu engineering admission entrance test is therefore not conducted but the website is maintained with the same initials. Students seeking admission has to register online submitting different forms and paying of fees. At the moment this site is not up and running but is expected in the first week of June. Just have patience tell them. Best wishes to you.