I'm a Lafayette Coney Island guy myself, but American Coney Island is very good as well. I will say they have a larger menu, although I have only ordered coneys and fries, which is what I get at Lafayette too.
I can also say that American is ""nicer"" on the inside and generally more decorous. You can't go wrong with Lafayette or American Coney Island. Both are Detroit Landmarks and serve world famous coney dogs.
A lot of the time, I will get a coney at Lafyette and come right next door and order one at American. And no, I'm not a fat ass (LOL) they're both just ""that good.""