Here is my answer to a similar question comparing Royal Caribbean to Carnival. I really like Royal Caribbean. The prices are still really good, but the food, entertainment, service, etc. is much better to lines like Carnival. It is an overall nice experience for the whole family.
I recommend Carnival, only if you can't afford the Royal Caribbean lines, or if you are wanting a "young" atmosphere. On Carnival there is lots of drinking, gambling, partying, etc.
Here is my answer:
I would definately say Royal Caribbean is going to be your best option. The quality of the cruise is a lot better. It is usually cleaner and the service is great. Carnival is a budget ship and it can show. You are going to see a lot of partying on board Carnival as well, and it can be unpleasant at times.
Royal Caribbean still offers a really fun cruise, but it is not non-stop partying. As the other person said, Royal Caribbean is really great. For the small price difference between the two, you really are getting a much better cruise.
Carnival is mostly for budget families with kids and college aged kids wanting to party. If you can afford to upgrade to Royal Caribbean I think you will be much happier. In my experience, I've never got off a Royal Caribbean cruise and been dissapointed, but I have been dissapointed with Carnival on more than one occassion.
I would check out:
http://cruisecritic.com/ to see reviews of both ships to see which you think will suit you better.
If it was me I would go with Royal Caribbean without question.
Hope this helps!