Disney is the only way to go, even without children
Granted, this was our first cruise, so I don't have much to compare it to, other than reviews from other cruise lines. But I must say that Disney will be the only cruise line I go on. Me and my husband went without kids, and even without kids we had a great time. There were enough activities for adults, and adult only areas that we did not feel like we were over run with children. We chose the late dinner so that there would not be as many kids, and we were not disappointed. I say this as being a person that not only does not have children, but I do not do very well with children, especially young children. However I am a huge Disney fan and really wanted to try a Disney Cruise.
The staff was amazing and did everything they could to make our cruise fabulous. You just can't beat Disney service, and that is one reason I don't know if I would want to try another cruise line. The other reason, is that even the adult events were very clean (no nasty jokes/cursing) and I always felt comfortable at the shows. We loved our Disney cruise and can't wait to go again. I think I would rather stick with the older, smaller ships only because it seems like it would be a little more comfortable especially in the pool areas. The larger ships still only have 1 adult pool, 1 family pool and 1 childrens pool, but have a lot more people on board in those pool areas.