A lot of the best British comedy is tempered with a melancholy and poignancy which sometimes translates and sometimes doesn't. Open All Hours, Porridge, Hancock, in particular, come to mind. Best of all is Steptoe and Son which, when you actually pay attention to it, is unremittingly dark and essentially about having the life crushed out of your aspirations. Very heavy for a 30 minute 'light entertainment' show, and ground breaking in many ways.
It's a common thread - it's largely what Fawlty Towers was about: a social climber who was always handicapped by his own crippling social insecurities and those around him. I think Cleese is on records as saying, in effect, that they quit while they were ahead.
My favourite British comedy of the last few years is Bluestone 42, which is about a bomb disposal detachment in Afghanistan. it's funny, it's clever and it doesn't pull its punches whilst being highly respectful of what those guys go through.
What else? Nighty Night from a few years back? It's very funny but extremely, extremely extremely brutally dark.
I don't really watch a great deal of American comedy, I have to admit. I'm going to buy the huge Phil Silvers Show boxset in the near future (Bilko being one of the best sit coms ever made,) and I like the Big Bang Theory but that's it. My mate keeps trying to get me to watch How I Met Your Mother, but I just don't get it. And I'm apparently the only person on earth who hated Curb Your Enthusiasm. I watched Scrubs for a while, but kind of got bored of the hyper-kinetic moralizing.
Now, Arrested Development....that was funny. And I loved 30 Rock as well. Bored To Death was brilliant too.
As for Python. Its funny as hell in places. Other, not so much. They took so much from that crop of comedians like Spike Milligan, Michael Bentine and so on who made it big when they came back from the war, and BBC radio comedy from the 40s and 50s is so sharp and so full of incredibly rich language and intelligence that you can really see where the Pythons got it from.
Of course, Milligan and Bentine took a lot of their inspiration from the Marx Brothers who in turn took their inspiration from American Vaudeville and British and German variety and music hall. It all goes around.