There is no comparison between the two place. Trinity (established 1592) is one of the highest ranking universities in the world. It is also one of the 'seven ancient universities', along with Oxford, Cambridge, St Andrews, etc, etc. You only have to look at the place to see that it's essentially Ireland's Oxbridge. Queens............mmmmm..........not so sure. If it's prestige you want, I'd say Trinity for sure. But comparing the two places is like comparing Oxford U. with Aston University. There's just no contest.