Hello,
There is no IIT in Tiruchirapalli. There is NIT Tiruchirapalli and IIIT Tiruchirapalli.
Choosing your college and your branch must be your individual choice considering your interests. Well, in your case, you have an option of choosing between IIT Goa and Mechanical engineering at NIT Tiruchirapalli. NIT Tiruchirapalli is one of the best NITs in India and IIT Goa is a new IIT. But here is another thing too. You should go for mechanical engineering at NIT Tiruchirapalli if you are interested in mechanical engineering. If you are interested in technical stuff like coding, you should go for IIT Goa CSE. Also, CSE is one of the most demanded branches of engineering because of its scope. CSE students enjoy an edge over other branches for placements in technical companies if they maintian a good academic performance in the college. So, these are a few things. Before choosing your branch and college, look where your interest lies. Choose your college and branch wisely.
I hope it helps.

Hello Aspirant
IIT goa is new COLLEGE and nit Trichy is one the top college of India . My suggestion is go to the nit Trichy for mechanical . If you are more interested in cse then you should go to the IIT goa .
Thanks