comparing anime (japanese) and cartoons (american) which includes adult cartoons:
i prefer anime. i like the complex storylines that aren't just meant for children. most cartoons are made for children which have very limited plots, with no complex stories to follow. even more adult cartoons such as family guy or south park---they don't have complex plots, each episode is different.
many anime even have deeper meanings, such as environmentalism and keeping people thinking about how they are living and how it effects the world. this is rarely found in american animation.
anime also has an art style i like, but i used to hate anime art styles, the tall skinny characters with the weird hair, but after getting into anime and manga i have gotten used to it and even prefer it. but within anime there are all types of art styles, my fav within that is the taller, longer characters, not the short stalky types. i also like brighter coloring and more realistic depictions.
since there are all sorts of art types in japan and america, its hard to really compare them. i just know that i prefer japanese animations, coloring, style, and whatnot, its hard to explain without comparing a specific anime with a specific cartoon.
sure disney cartoon movies are good, i grew up on them and like them, but only for those types of movies. so i guess i prefer certain types of animations in certain mediums or certain genres. but when it comes to non-movies, series i prefer anime for the storyline and because in Japan they aren't specifically aimed toward a certain age group (some are, but not most). i hate the stories and animation of most american shows on cartoon network or the disney channel (though i do like fairly odd parents on nick), they plots aren't just stupid (in my opinion) but the characters and dialog are bad too.
i guess im just used to shows that are abit more complex now. i have come to expect good characters, a good mix of comedy and seriousness, good complex plot, and all the other things found in anime. i also enjoy anime because, to me, its like a window into Japan and its culture. sure not everything is realistic but it is still interesting to see. in cartoons, all it represents is my culture, a culture i already know about. i like new things, and to me american animation is old and anime is new to me which makes it interesting.
*i am a 21 year old female, which might be important when taking into consideration my taste and preferences.
hope that answered your question.