What I have seen -- from the behavior of your celebrities, from your books, from your reality TV shows -- is that the middle class and lowest class of both cultures are about as equally poorly-behaved. People say, "British people are classier." Well, I'd say Americans and Brits are equally classy (or un-classy) -- that is, until you compare the upper class of both countries. America's elite are often just elevated trash (i.e. Paris Hilton, etc.) whereas the elite of England are generally a classy, well-behaved bunch.
So, yes, when you compare the people that count, the British are classier.
I think, also, that people in England are generally better edcuated. They are also more cultured, as they are exposed more readily to the influence and history of Europe, etc.
I think Americans are more patriotic. It's kind of programmed in Americans to think their country is better than every other country -- it's a big country, it's a powerful country, it's culturally charged. Americans have Hollywood, so they tend to feel like they drive popular culture.
Also, the food in America is generally better taste-wise, but it's not very good for you. British people eat the strangest things -- but at least it's not all deep fried!
Americans are more superficial. Maybe it's the Hollywood influence, but almost everyone here is camera-ready. We expect good grooming and streamlined presentation -- thus the prevalence of orthodontics and plastic surgery.