Last time I checked Europe used PAL
America uses NTSC
and they are not Compatable with one another.
You are some what right. You can't take a Europe disc and play it in an American xbox and vice versa.
BUT that doesn't mean you cannot play with a European over Xbox live, i have done that many times. It works in 99% of Xbox games, so most likely, you will be able to play with your friends across the world