We've cruised Carnival, RC, Princess, and NCL. Our findings are that RC is our most preferred line, with probably Princess a second.
Each brand (like any hotel brand) has its reputation, strengths, and weaknesses. Our impressions:
Royal Caribbean has the most beautiful ships. While we've not yet been on the Oasis/Allure class, we love the Voyager class of ships. Their ships have real wood, granite, and marble, and the art is beautiful. The 10+ story atriums are spectacular and gorgeous. The line is geared to mainstream travelers and famiilies - not a party boat but not a grey-haired boat, either. Entertainment is excellent. Foodies claim the food iis mediocre. Since we're not foodies, we don't care, but it could be important to some.
Princess is like RC with a bit less grand/pretty ships, and just a little more sedate. Still very good, with good entertainment and high quality ships. They have the best itineraries at more exotic locations.
NCL (we were on the EPIC) was fine and we liked the ship. It looked nice but we found that when you actually touched the decor, things weren't as high quality as they looked at first. Things like wood posts that are really plastic, or plastic appliques in the decor. Just a bit cheap. We found their food very good - probably the best buffet on a ship. LOTS of nickel and diming - more than other lines. We found the ship's excursions on our European cruise averaged 1.5-2.0x the cost of comparable excursions on RC or Princess. Kind of like they lure you in with a good cruise fare, but then make up for it by ripping you off on the excursions. Needless to say, we ended up doing all of our own arrangements for touring at ports.
Carnival - among the best food we've had. Ship was ok but definitely more of a cheaper Vegas hotel decor. Crew was good and entertainment was excellent. Would cruise them again, but definitely not our first choice.
We've found all our cruises to have generally great crews and service, although there can always be a bad apple or two.