I'm a Brit brought up with football (soccer) my #1 sport, a few others I like, and games like baseball as "those stupid American" sports, I became a huge baseball fan about 5 years ago (after going to a Dodgers game).
The biggest difference to realise is that in European countries travel distance for fans is SO much smaller. Leagues/cups here have minimum %s that teams must sell to the other team's fans when playing at home, and big teams have big number of fans who regularly travel, as well as it being a much easier "let's go to one away game" choice for other fans who don't regularly travel.
I'm not sure which I prefer. I've loved chatting with Giants fans in Dodger Stadium, but the atmosphere you can get with two groups of fans which are in separate areas... obviously there is some extent of possible violence between fans in European stadiums (in some cases police may need to keep them separate outside the stadium before/after the game, in other cases after the game you'll hear some shouted jokes at the other team's expense but see opposition fans walking next to each other to get to/from the stadium). Personally, for sports like football in UK/Europe, even if there was exactly 0% risk of any problems between the fans, I'd still choose to keep them separated for the atmosphere. So actually yes I am sure which I prefer. It just isn't viable in a country the size of America.