Well, it may be hard to compare because we went on one of Disney's smaller ships... but at the same time we also went on Royal Carribean's smaller older vessels. So here are some comparings between the Disney Magic and Grandeur of the Seas:
So here you have Disney themed characters roaming the ship vs no characters on the Grandeur. I believe some of Royal's larger ships will have Dreamwork characters but we weren't on that boat and my kids aren't as familiar with those characters (like Shrek). So from my daughters point of view... princesses win.
The actual kid program on both ships are very good in my opinion. I was pleasantly surprised at how organized Royal Carribean's kid program was. They had plenty of activities and crafts and my kids seemed to have lots of fun every time they went. The actual play area where the activities were held was much smaller on Royal.
Going off season was a plus for both ships since the programs were less crowded.
Our family of five had to squeeze into one small room with a balcony for both ships. Royal's room was slightly larger as there was slightly more walking room once all the beds were pulled out. However, since my girls were not used to sleeping in the same bed and kept kicking each other and keeping each other up, we ended up having to split them up and each slept with a different parent instead. Whereas on Disney Magic, they had two separate pull out type beds so each child had their own space. Plus Disney had a curtain to divide the kid section from the adult bed section, so it almost felt like two rooms.
The other plus on the Disney ship is they have tiny bathtubs in the bathroom so you can bathe little ones. Based on that, I can tell they definitely cater more to families with small children.
I loved the wave phone on the Disney ship. Since you can't really use your mobile phone once out to sea if in international waters (unless you want to pay a fortune), it was super convenient to be able to call one another on the wave phones provided in each stateroom. I used it to communicate to my husband as well as other family in other staterooms that we were travelling with. You get two phones per room... so huge huge plus! I'm not sure if any of Royal's other ships have this feature.
I think Royal wins in this category overall but only by a slight margin. Royal had more options in the buffet dining. However, overall quality of the food during the regular sit down meals were probably about the same on both ships in my opinion. Disney's Magic did have more variety in ambience since they rotate you through three different sit down dinings which had different themes. That made things more interesting/entertaining.
Other Ship Activities
Both ships have pools for kids as well as for adults only. The kid pool on the Disney ship had more fun elements like a slide and fountains for little ones etc. Royal has a climbing wall which my husband loves. Now Grandeur was one of the smaller and older ships in the Royal Carribbean line and they did not have a movie theater which is usually where I go after the kids are asleep. So I was disappointed at that. Disney Magic did have a theater and they were playing fairly new movies like Brave and Avengers on there back in Sept 2012 and you can watch it in 3D. No casinos on Disney which in our opinion is a plus... don't have to walk through a really smoky area just to get to another part of the ship.
My kids loved the Disney shows. I don't think we let them watch any of the Royal shows since they seemed more interested in just going to the kids clubs for the activities they had there. Personally, I also really enjoyed the Disney shows and found only some of the Royal Carribbean shows very entertaining but I suppose it depends on your taste.
Disney costs a whole lot more.
So overall?? Both were good experiences... when I ask my kids, they liked the Disney cruise better. However... for the value and and the difference of price.... is it worth it? Would we cruise with Disney again? Maybe just to try one of their bigger ships... but will have to plan and save for it... and will likely be a while...