We just traveled for our honeymoon the Celebrity Century. We considered Royal Caribbean, but after doing the virtual tour on Celebrity we were very impressed by the recent upgrades.
I've been on Royal Caribbean before and the rooms on Celebrity were MUCH more spacious. Lots of closet space so we were able to unpack as soon as we got there. The bathroom was also bigger than RC. Other little service niceties were when we came back to the ship after Grand Cayman, they were waiting for us at the dock with cold juices and cold washcloths. Even though the food was pretty ordinary, the service was great. The room service was decent though. We had GREAT tablemates for evening dining and had a ball with them all week long! Not sure how they select your tablemates but ours were GREAT! We even exchanged contact info at the end of the cruise so we can stay in touch.
There were little decor things here and there which others have complained about, but it really wasn't a big thing to us. We also got a great deal so that helped a lot. We were on the fourth level in an oceanview and it was really a nice location. Some may prefer to be up higher, but we were right off of the elevator and also right in the middle of everything going on on the ship. The other advantage over our RC trip 5 years ago, was that there were THREE sets of elevators: the front, the back and in the middle. The biggest thing we noticed is that we were in almost NO lines the whole vacation. If I didn't know that the ship was full, I would've thought there were less people.