I would give Celebrity a slight edge on dining and service. Rooms are very comparable, but that is toward the bottom of my priorities since I rarely spend many waking hours in a cruise ship cabin. I would consider Celebrity more elegant. If you are an active person, Celebrity can be lacking in activities and even the Edge class ships the entertainment is at least a notch or two below Royal Caribbeans's largest ships.
Celebrity's entertainment is fine if you are satisfied with mainly singers and acrobats, but it really does not compare with Royal's Oasis/Quantum/Icon class with Broadway shows, Aqua Theater, Ice Shows, Comedy Clubs, etc. I also believe that Royal's loyalty program benefits are better (Diamond and above) vs Celebrities (Elite and above).
I do believe Celebrity has the edge in unique itineraries that interest me, but if the ship is the primary destination (like most Caribbean itineraries) that I have been to many times before for decades I prefer the larger Royal ships for the entertainment and activities and specialty dining options.
The bottom line is both lines have their place based upon itinerary and activities that you want to do.