From what I've seen, there tends to be a lot more individuality on NA. There's a LOT of variety, and a lot of people trying out new play styles, new builds, new tricks and tactics, etc. That's why we have more 'flavor of the month' type builds, like horse crossbowmen and pure throwers. People are always trying to find an edge and experimenting with new stuff. Likewise, NA players tend to ignore team play a lot of the time. They're more interested in dramatic exploits and exciting fights, so there are a lot of heroes. Also, it doesn't help that there are only a few big, worthwhile clans on NA.
By contrast, EU players tend to follow tradition. They use tried-and-true weapons, builds, and tactics. Danish greatsword, heavy kuyak, strength builds, heavy horses,shield walls, cavalry charges, etc. These guys take a straightforward cookie-cutter approach, stick with their team, and fight the good fight rather than running all over the map on their own. The EU servers are also a little more populated than NA, so it feels more like a big battle than a skirmish.
There's no real good or bad to it, they're just different.