Some kids shows are boring to an adult audience because they are very heavy handed with moral themes. I remember watching an episode of the animated remake of Sabrina the Teenage Witch. I liked the original series, but the remake sacrificed plots and nuances for monologues on why you should listen to your parents or something. I read an excellent article in the LA Review of Books' blog
http://tumblr.lareviewofbooks.org/post/24379111143/better-to-light-a-candle-than-to-curse-the-darkness) that talked about how parents should probably try to find books that their kids like rather than trying to find books that will teach them a good lesson and that their kids will like (because the former will encourage kids to read, and maybe the lessons that they need aren't the ones that the parents think they need). I mostly agree with this sentiment.
One of the reasons that I enjoyed Avatar was that the ethical elements were integrated seamlessly into the show. Moral issues were presented as challenging problems to work through where the right answer wasn't always clear at the outset, much like in a show with social and political commentary like BSG.
One issue with many shows, though, is that the characters have very flimsy ethical philosophies (which is, perhaps, symptomatic of our society as a whole). That is, the protagonist in a drama made for adults will often want to do the right thing, but in many cases, they wander aimlessly to try to get to this right thing. They might plan an assassination attempt for their own survival and, after 20 minutes of soul searching in the show, decide that "it's not enough to survive. One has to be worthy of surviving" (that's a BSG reference) and call the assassination off. The characters haven't analyzed their values or figured out what they believe to be right or wrong, so they keep changing deep-seeded beliefs. More than anything else, these shows promote the idea that it's okay to go through life without figuring out what you believe until the last minute. I think that's bad.
Avatar succeeds on both of these notes because the world isn't simple, and choices are hard to make and deal with complicated ethical issues, but the characters have consistent ethical philosophies and when a character changes one of their beliefs, it only happens with hours worth of development and in few instances. Off the top of my head, I can only think of one character that had a major change in values, and that was the result of three full seasons of character development. The protagonist, for instance, is a humble monk (in many ways, an allusion to the Dalai Lama), secure in his vegetarianism, his refusal to kill, and in his search for peace.
As far as I'm concerned, the movie adaptation, "The Last Airbender," doesn't exist.
Just this year, though, a sequel to the animated series was released. This was the first time in a long while that I have watched a TV series that was still being aired and produced while I watched it (meaning I can't always just go to the next episode). The sequel, Avatar: The Legend of Korra, is good. It's very different, and I haven't seen enough of it to write a good critique, but I like it.