My fellow cruisers have said it all. Both are great--itineraries and pricing usually help us make the choice. Some folks also compare onboard features. For example, I believe that some of the Celebrity ships have the Thallasotherapy salon and spa, while som of the Royal Caribbean ships have the rock -climbing wall. So you'd have to compare brochures and see which of those "signature" items is of most interest to you.
We've been cruising since our honeymooon and I can honestly say that we've had great experiences on all lines (except Carnival--which was OK but too "party-hearty, hey hey hey, aren't we all having a GOOD TIME" for us. We prefer not being reminded by the staff every minute of what a good time they are giving us..)