The problem with children's zoos for me personally is most of the time they're just not worth the visit. Omaha's is very well done and naturalistic, but there's so much more to see at that zoo I don't think it's worth the visit. There are four animals, goats, budgies, prairie dogs, and squirrel monkeys so I usually don'y visit that part.
I think children's zoo should have both domestic and exotic animals, but for the place to be called a "children's zoo" there should be exhibits that the kids can be a part of.
For example bubbles for prairie dogs and meerkats, crawl-through tubes and for penguins and otters, and climbing structures to get up close to monkeys and birds.