I'm a Brit married to an American, and it's very interesting, because I'm also a comedy geek. There's very little Brit humour that my wife enjoys. I like a lot of both Brit and American humour. I do appreciate the differences though. I think perhaps the difference is best illustrated by Steptoe/Sanford and Son.
In the orginal UK version of this comedy that was eventually popular on both sides of the Atlantic, there was a lot of pathos, a lot of almost-tragedy. It was a situation where two people were trapped together by the bonds of love and family, and driven apart by the immense personal differences in their characters. The very first episode of this show showed the son in tears of frustration and rage as he tried to escape his father's small world.
When it transfered to the States, the writers were told it would never fly for a US audience. It was lightened, made into more of an aspirational comedy, and did extremely well.
That, essentially, is the difference - British humour is the humour of losers; they may be gallant, they may be loveable, they may be intensely frustrated or tragic, but ultimately, they're losers. You can see it throughout British comedy archetypes - Tony Hancock, Harold Steptoe, Basil Fawlty, Del Boy Trotter (most popular Britcom character of all time), Victor Meldrew, Dave Lister, David Brent...all of them flawed, some of them doomed, all of them ultimately losers. Compare them to US comedy archetypes - Bilko, Lucy, Frasier, the Cheers gang, the Friends...they're all much more innately positive characters, all potential winners, usually a lot more wisecracky and dependent on lines, rather than tragic inability to achieve.So basically, that, I think is the line that can be drawn between UK and US humour, and what it shows us about the comedic appetite of both nations - Brits like their comedy heroes to be likeable losers (reflecting the post-war smallness of our world and ambitions). Americans tend to like their comedy heroes to be wittier, faster-paced potential winners, because losing, ultimately, isn't funny in America.
Sureal comedy like Monty Python and the Goons of course is the comedy of words and/or twisted situations, and there I think there's less cultural difference, because, for example, the idea of a government ministry dedicated to promoting silly walks is a funny concept irrespective of WHICH national government it might be.