Having been on many Carnival cruises and RCCL cruises, I have to say I lean more towards RCCL. However, with that said, I also have to say I feel like over the last 10 years RCCL has diminished somewhat in their food quality whereas Carnival has tried very hard to improve. While the gap is narrowing, I still think RCCL has an edge. But food is very subjective and what one person loves, another will hate.
And having been on the Liberty of the Seas, I can say it's a very nice ship with alot of amenities. However, the food in the main dining room does leave something to be desired. The specialty restaurants are very good. And the Hoof & Claw English Pub is my favorite bar. Shows were good, especially the ice show, which is something not to be missed.
As Trip said, both have their die-hard fans, so you'll really have to decide for yourself as to which one is best for you. And therein lies the best part of cruising.