Interestingly enough, Royal Caribbean and Princess would have made a better pairing. They would have been much like siblings in the same family.
Carnival's management style over it's acquisitions seems to be to let them operate as they always have. Even though Princess is now under the Carnival umbrella, it is still Princess.
Royal Caribbean, on the other hand, almost ruined (in a business sense) Celebrity when it acquired them. RCCL tried to make Celebrity into RCCL instead of letting Celebrity continue to be the fine operation that it was.
It's been a combination of RCCL missteps, and Carnival business savvy that's led to the current state of the cruise industry. That being Carnival as the largest cruise line company, as opposed to Carnival and RCCL being roughly equals.
I'm a RCCL fan, but as much as it pains me, I have to call it like I see it!