Carnival isn't always cheaper. Royal Caribbean spends a lot more on their ships, entertainment, innovative activities, than does Carnival.
For 2012, Carnival and RCI have essentially the same number of berths (around 62,000) although Carnival has them on 24 ships versus 22 ships for RCI. They both sail full on virtually all cruises. Carnival probably has more short cruises than does RCI (I didn't check), and that can skew the passenger figures if the statistics are not compared equally.
People like to say Carnival offers more 'value', and I've said it too. I'm not so sure anymore. I've looked at what I've paid for similar cruises on both lines and the costs are also similar - at least for us. I am including onboard charges.
I can also say that RCI blows Carnival away in how they treat suite guests (as does Norwegian). I know everyone can't afford suites, but on Carnival there are essentially no special perks other than priority boarding, while on RCI I have priority boarding and debarkation, concierge service, private lounge on the ship with free drinks and in some cases menu service for light meals.