From my personal experience, the directors on Carnival were better, the actual teen facilites on Royal Caribbean were better.
On Carnival Victory several years ago, we couldn't even ever have dance parties or anything because O2 was right next to the spa and we'd have all the old dinosaurs (people who I would never suggest to sail on Carnival in the first place) complaining about the noise when they were trying to do whatever it is old people do in the spa. One night the teen director did get us out by the pools for a dance party out there and it was great, at least until it started to rain.
The director on Royal Caribbean had more of a babysitter attitude. The room itself was larger and better than Carnival, but she was just acting as though our parents were sending us there as if it were day care service.