First off, in America, Autumn is not some weird British word for Fall, it's a synonym. I see both words used regularly.
I use American because i'm American. I also understand that letters and words are arbitrary symbols representing arbitrary sounds that we decided to give meaning to. So none is truly better or worse. However, if I were to evaluate objectively, I would say that sometimes the American is better, sometimes the British is. For example, (And to delve into the wacky world of pronunciation as well) British say, "Herb" while Americans say, "Erb". I have to go with the Brits here, in the words of Eddie Izzard, "Because there's a fucking H in it". Meanwhile Americans spell it, "Center" and Brits spell it, "Centre". Unless the Brits are talking about the kind of gun the engineer builds in TF2, that spelling is horribly unintuitive and silly. So basically, both have there strengths and weaknesses.
To go on a related tangent, I think that there's another interesting language trade-off. British language has developed a certain sense of class about it, mainly because America is the melting pot, and looks to other cultures for inspiration in a lot of things. This is in exchange for every British term for Car related thing, used by everyday people, being inferior to the American term. Or maybe that's the trade off for American cars never being able to turn properly. Or consolation for having to tolerate NASCAR.