I can't be friends with people that call anime cartoons. I mean, how dare you disrespect anime like that.
On a serious note though, they aren't comparable. Anime are Japanese animated shorts or films, often containing subjects, scenes and stories that aren't for children. Cartoons on the other hand or mostly very much for children.
I was an anime fan from very young, before I even knew it was called anime. I always watched Dragon Ball Z and Naruto as a child. The first anime I watched when I knew what they were called is Attack on Titan, one I do recommend.
Give them a chance, you'd be surprised how entertaining they can be.