I have never been on Royal Caribbean, but I really like Carnival. I just like the overall atomsphere of their ships and what they offer.
Carnival has won some recent awards from Porthole Magazine.
-Best Mega Ship- Carnival Freedom (I was on that ship and it was very fun!)
-Best Shore Excursions
-Best Short Duration Cruises
-Best Value-For-The Money Line
-Best Children's Program (If you have children, their programs are very fun for children.)
-Best Main Dining Room Cuisine (Yes I think their food is very good)
-Best Entertainment (I really like their Las Vegas style shows. Their shows have won multiple awards)
-Best Mexican Riviera Itineraries
These are just a few things that Carnival does great, but there are many more.
Sorry I couldn't help you with Royal Caribbean. I have never cruised with them. Hopefully someone else can help you.