Not all anime series are about Fan Service. There are quite a bit of Mature (No School girls with panty flash etc.) series like Attack on Titan, Fate Zero, Psycho-Pass and more. You don't have to watch all anime if you can't stand those types of fanservice, just ask some anime fans for some good mature series.
Plus I prefer Anime over Cartoon because most Cartoons are just episodic comedy filled series. Don't get me wrong, I laugh to quite a few of their jokes, but that's basically all that Cartoons have. There are anime that are like that, but there is also anime with a good storyline and amazing characters that just brings you to awe.