(British OP)
I agree that British sitcoms (not comedy generally) were superior for a couple of decades, but think we need to give modern American comedy much more credit; Seinfeld, Curb Your Enthusiasm, Larry Sanders, various animation series, etc, etc have established them back at the top. I can't see the UK as that competitive these days.
That's not considering American standup, movies etc which leave us in the dust.
What We Do in the Shadows, except it's NZ really.
Oh there are certainly some excellent American comedy shows..
Seinfeld, Curb, Arrested Development, Modern Family, The Office (US), South Park, Parks and Rec, 30 Rock, Frasier, Fresh Prince, Friends, How I Met Your Month, Futurama, Simpsons (OG) and then there's not a lot more on the bench unless you include the lesser remakes of British shows.
A lot of them aren't funny or aren't satire.. just look at the Shameless remake - they turned that into a character drama when it was a sitcom.
America has more of a stand-up culture I feel.
I wonder if it's because the news in America is pretty much fiction that they basically don't have political satire as a genre outside of the topical news shows (Daily Show / John Oliver) which are honestly more like real news shows than comedy at this point.