I just came off the inaugural sailing of RCCL’s new Liberty of the Seas yesterday – she’s the sister ship to the Freedom of the Seas, the two largest passenger ships in the world. She’s a beautiful ship with everything and more than you could ask for. This is my fourth sailing with RCCL in the past two years (my wife and I are in the "Premium" level category) and I’m here to say that "bigger does not always mean better"! I find the food quality, service, menu selection (in both the dining room and for room service), and attention to detail, to be far superior on Celebrity (we are "Elite" level here). I also like the ship layouts much better on Celebrity.
Consider this – Celebrity uses a three elevator bank layout on almost all of their ships – that’s one bank forward, one mid-ships, and one aft. RCCL uses only two – one forward and one aft. So your mid ship cabins – the most desirable location on any ship – and where we just were on the Liberty – required us to walk to the forward or aft banks of elevators any time we wanted to go anywhere on board! My wife and I are in good shape, but I would not recommend the Freedom or the Liberty to anyone with health/walking issues.
However, to answer your question directly, my favorite RCCL is the Radiance of the Seas, ("known as "a ship of light" for all the glass used in her design), and by far, my favorite Celebrity ship is the Century – even more-so since her recent $55 million refurbishment!
I hope this information is helpful to you. One final word of advice, give your local travel agency a call and ask to speak with a Cruise Specialist. There’s no additional cost for their sevice and their information and advice is very valuable.