Here is possibly the single biggest difference between the lines.
We are activities people. We LOVE to participate in all the shows, trivia games, crafts, etc. For us that is often half the fun of cruising.
The Disney Navigator is jam packed full of things to do. Often you have to make a hard choice between two (or more) appealing activities. The kids have even harder choices sine their schedules also generally have lots going on. On Disney, the cruise staff is super energetic and engaging. They really WORK at each activity. They are out on the dance floor (in costumes) dancing with the guests, they are talking to you in the hallways, they are WORKING the crowd to get more participation at whatever, etc., etc. Really, more than anyhting else, the cruise staff is what makes a
Disney cruise so much fun. This cruise was no exception to that rule. We had a great staff (and a shout out here to James who was extra fantastic

).
For those who have not cruised Disney, the games, etc are often also rally set up well. There are game shows like Mickey Mania, Who Wants to be a Mousketeer, etc which all have sets with props and cruise staff in costumes to match, etc. It really makes it feel special. There are also more basic things like trivia, but other than the "family crafts" (which are pretty much Oriental Trading Company foam things) we always find everything to be very well done. Our one complaint in the past was that questions tended to repeat (in games, trivia, etc) from cruise to cruise. Disney FINALLY seems to have fixed that problem and we did not see a single repeat from last year at all
Royal Carribean has more of a general set of activities. At any given time less than half as much structured stuff is going on as on a Disney ship. To give you an example, only ONE cruise staff team member works during the day on any given port day. There will be 2-3 activities total on a port day from morning until dinner time. Usually 2 trivia games and possibly a scavenger hunt or pool game.
Some of the staff is more engaging than others. Most were friendly and willing to chat, but not anywhere near as enthusiastic as on
DCL. Accents were often pretty difficult to understand too, which made trivia frustrating for everyone a few times. One (JP) made it clear he wanted to be in and out of games as soon as possible (refusing to wait for a second group who asked to have a moment to go to the restroom before starting trivia--we were the only other people there and WE said to please wait, not giving long enough to write out answers, much less discuss them before moving on, cancelling activities when the pool deck was full when no one came up to him to ask what it was--no announcement was made, etc).
NO games or shows had any sort of elaborate set up like on Disney. The Love and Marriage show involved just normal chairs set on a blank stage (whereas on Disney the same thing has special "love seat" designed just for it).
One thing we did appreciate was that there were a variety of different little prizes you could win at various times instead of just "winner" medallions (key chains, pens, highlighters, t-shirts, hats, passport holders, etc).
Another problem was inconsistent labeling of and enforcement of adults only activities. Some things (like the love and Marriage game show) were labeled ADULTS ONLY but then large numbers of children were allowed in anyway. Other things (like the Battle of the Sexes) were not labeled adults only and yet all the kids/teens in the room were told to leave (and then they could not get enough people and cancelled it). RCI really needs to get the labeling right and then stick with what they say.
Overall, Disney is the clear winner in this category
