I have cruised 4 times on Royal and 9 times on Celebrity. I would say that Celebrity has better service and better food as well as a more refined atmosphere.
I will say that the larger Royal ships do have more activities and more variety in their entertaiment.
Carnival Liberty New Year's Eve 2007
Liberty of the Seas 5/2008+11/2009
Allure 1/16/ 2011
Independence of the Seas 12/29/2013 Top-notch!