Hoping this doesn't make me sound pretentious, but I don't think animated movies are necessarily kid's movies. Child-friendly or child-appropriate does not mean that they are not perfectly legitimate adult entertainment. It doesn't have to include sex, violence, and strong language to be adult.
On that note, I watch and enjoy both. I consider kid's movies to be ones that do not contain particularly complex or adult themes, or do not have a particularly adult sensibility. For example, Winnie-the-Pooh is a kid's movie, since it's a slice-of-life, isn't-it-great-to-be-t ogether sort of film. Heart-warming without being sentimental mush for adults, and gentle, positive entertainment for kids. The Emperor's New Groove is a totally child-friendly movie with an adult sensibility - it has nothing inappropriate, but it's so self-aware and so mocking towards the unlikely friends road movie genre that adults will find far more to enjoy than kids.
So... I watch animated movies all the time, as well as everything the Muppets put out, and I'm furious at Disney for sitting on the DVD releases to all of their old cartoon shows.