I don't have children and I've been on Disney three times. I love it. It's a total different experience from the other cruise lines. They don't have a casino for one thing. The dining experience is unique. They have three different dining rooms and you rotate each night to a different dining room. Your wait staff rotates with you.
The production shows are fabulous, they are geared toward Disney themes and movies. They have a regular movie theatre onboard and show current Disney movies.
I have never found all the children onboard to be a problem. Disney does such a great job keeping them occupied. There are plenty of adult activities. Adults have their own pool and children aren't allowed in the lounges after a certain time at night.
Disney's private island Castaway Cay is great. There is a private beach for the adults there too.