Disney all the way, absolutely. Not that we'd never go on a different cruise but if we have the choice, Disney. The first cruise my husband ever went on was pre-kid with my mom and younger sister. We didn't see many others without children but that didn't matter. There was So Much for Everyone to do. The kids seemed to Love the kids areas as we hardly ever saw them. The Adult Only areas were truly, adult Only. The staff was so friendly, just beyond compare. Like at the park, when they are taking your picture, they'll offer to take some with your camera (or you can ask and they will). This was great and even though we had nice ones on our camera, we still ended up buying a ton.
Cut to the Carnival Cruise we went on. It was good. I mean, it was much cheaper and so we were able to get a great room with a deck which was completely awesome. But the adult only areas always had kids in them and there just didn't seem to be as many things for the kids to Do as there were always groups of them running around screaming, etc. They also will NOT allow you to take pictures of the professional ones and one of them even grabbed my moms arm when she went to take our picture. We did not buy ONE from them.
The quality of entertainment was also vastly different. On the Disney cruise the shows were broadway caliber. Really beautiful, funny, fun. On Carnival, they were pretty cheesy. I enjoyed all the different trivia things they had on Carnival but the actual shows were WAYYYYY better on Disney.
My husband, after the Carnival cruise, said he didn't care to take anything other than Disney cruises from now on. Lol.