I'm a proud American who avoids the practice some have of automatically ascribing superior attributes to anything and everything European. I have, however, readily noticed the general difference in the way people dress, at least as far as middle to upper-middle class people in casual settings, like cafes and other public places.
When I'm in Europe (my limited experience has been mostly in the Mediterranean regions) I see very little garish logo clothing, and almost no ball caps. I see either nice shoes or really hip sneakers rather than generic Nikes. I see almost no "gangsta" wear. (With teens, all bets are off, though.) I see nice shirts that button, a lot fewer basic Polo shirts, very few mass-market t shirts. When I see fleece it's styled really cool. Cool jackets and sweaters.
Most importantly, I see clothes that FIT. This may be related to seeing very few overweight people, at least compared to here. But things just seem to be tailored better there.
My last trip to Europe was what finally motivated me to do something about my wardrobe and style, and to start hanging around here.