I have sailed the Destiny and Imagination, and I absolutely LOVE Carnival. With the exception of one or two people, my service on board has never been anything less than exceptional.
I sailed Brilliance of the Seas, a Radiance class RCI ship (my first Royal ship), in June and have to say it was great and the smoothest cruises I've ever been on. I really like RCI. I heard on that ship from people who have cruised the Voyager class ships that they are amazing. Royal lacked in some areas service and food wise, but I will definitely sail Royal again.
Whichever you choose I'm sure all of you will love it. Hope this board helps