From what I've seen American audiences at stand up comedy events seem to cheer much more than they laugh, as opposed to British audiences who seem to laugh and only sometimes applaud, why is this?

The old British reserve.

Maybe the British have a more laid back attitude.

Just a tiny observation from the very, very few British stand up comedians I have seen, versus the many, many American stand up comedians I have seen….

I think it’s the content. I think British comedians have more joke telling & silliness (which requires laughter as a sign of approval). The American comedians I have seen (George Carlin, Robin Williams, Lewis Black etc…) their material has a lot of political content & they poke fun at the problems in America. It is funny, but instead of laughing uproariously, we applaud like mad as a sign of our approval & agreement with their statements.. it’s our sign language for “Hell yea!”

British comedy is more dry, sometimes more cerebral, and sometimes more off the wall silly.
American comedy is more acerbic, political, more more charged with sexual and racial tensions.

One would expect such different responses to material that is so different.

What @rpmpseudonym said.

British humor is mostly, from my understanding, based on dramatic understatement and subtle irony and sarcasm. American humor is based on hyperbole and punchlines.

The two distinct reactions sound like reasonably measured responses to the respective humor styles.

@Dr_Lawrence and @Fiddle_Playing_Creole_Bastard described the humor differences really well.
Americans are naturally more loud and outwardly reactive, much more uninhibited. Maybe it is all these wide open spaces !

Cultural differences. I love both American and British humor.