It's probably a combination of a lot of factors:
1) Architecture, I'm sure, plays a role.
2) Experience is another: Parkour & Freerunning have had more time to develop overseas.
3) Culture, of which music is a subdivision, may also be a factor. We're dubiously blessed with the "American Spirit." Go big, go fast, and do it all RIGHT NOW!
4) The biggest contributor to me though, is probably in the WAY the discipline has spread. In the UK, it started out with just a few guys, and those guys had time to train slowly, methodically, and develop their skills (and more importantly, their mentality) before many other people knew what this whole "Parkour" thing was all about. They got to start the initial communities, and set an example that helped inspire the movements and styles of others. It also seems as if many people learned person-to-person rather than via youtube tutorials and the like. (Easier to do in a smaller country, I imagine)
In the US, Parkour has spread very quickly to all corners of the country and is exploding without the kind of guiding influence from preestablished communities that the UK experienced. We don't have as many "role models," I guess you'd say, to influence the way we move and think about parkour. Here you get lots of kids in suburbs all over the country copying what they see in youtube vids without knowing anybody else who does it and that they could personally learn from.
Maybe the difference isn't so much "European vs American" styles, as it is "2nd Generation vs 3rd Generation" styles. It could be a natural difference in the development of training styles due to the spread of parkour to wider, mostly youtube-learned audiences. If that's the case, I think it's likely that as the new American communities continue to draw in and guide newcomers, we'll see a rise in the number of burgeoning traceurs with similar training and "flow" mentalities to the UK and French scenes (4th Generation, perhaps?) ...although I doubt we'll ever be completely free of the "GO BIG RIGHT NOW" mentality that seems to be at the heart of American culture, LOL.
