Everyone is comparing anime to disney. Disney makes cartoons for kids and they're good for kids, just not good for other age groups. Anime is made for all age groups and for everyone. I believe that everyone can find an anime that is absolutely perfect for them no matter what they are looking for. Can't say that for disney.
That's true to a degree. It's tough to compare anime to anything american because here cartoons fit mainly into two catagories: for kids, or for adults late night adult stuff e.i. South Park, Family Guy, Venture Brothers... which are for adults because they mostly rely on coarse adult gags.
A better comparision would be Disney/Studio Ghibli. But Ghibli's stories are still better for the same reasons... good plot, good characters, and realisitc situations that aren't toned down too much, even though their for kid's too. Sure you don't want to give kids nightmares, but you shouldn't rob them of solid stories about good and evil. ( I have a favorite CS Lewis quote about that topic).
It's not well known but many of these old fairy tales that used to be commonly excepted children's tales are quite gruesome. The original Disney took a lot of these old tales, and updated them, toning them down a little, but not so much to lose the gravity of the stories. Nowadays Disney has simply stopped trying. They don't want to offend or frighten. They want to please everyone and they please no one.
With Michael Eisner still in charge, it is highly unlikely Disney Animation will recapture it's grand storymaking days. Have you seen the commercials for it's upcoming CGI movie "Chicken Little"? Ugh.
What? You're kidding! Didn't they learn anything from Home on the Range???