There's no comparing the two, American sports fans are generally extremely civilized and relaxed compared to soccer fans in many places around the world.
Years ago I went drinking across Europe and I wasn't even following any team, I just like to drink on baloney cafes and I incidentally watched them do so many insane things, bottle fights, bottle fights between buses like capital ships squaring off with everybody inside of each bus lobbing bottles at the other bus, bottle fights contained completely within a singular bus, fighting cops, driving Italian cops past the point of sanity where they just ran around screaming and hitting everybody they saw with billy clubs, hitting each other with car antennae, trash fights, trash can fights, trash and trash can fights with cops, what appeared to be an organized mass spitting, dueling jason vorhees (I think), stealing deployed teargas canisters as souvenirs, fighting over stolen teargas canisters while they're still hot, and so much more drunken stupidity.
And at the games themselves, personal space does not appear to exist and I kept hearing children screaming for help, but I never saw any.