When we are talking about good themes and good story and good way of representing it and in a mature sense, definitely Japanese Anime.
Have you heard of the Gibli Films. Top notch Japanese anime movies.
And who doesn't know One Piece, Bleach, Naruto, One Outs and many more great anime.
In Japanese anime its more like you are entitled to think.
In US Animation its really for kids, where in not that much of thinking is needed when watching them.
But the thing that I like in US animation is there whacky cartoons especially the one's in nickelodeon and some Disney cartoons.
Like Spongebob, Fairy odd Parents, Phineas and Ferb.