The Royle Family was superb, but I think it's incredibly British; the family, the pop culture references, everything harks back to a certain way of life which is typical of urban Britain.
The best British comedy show in several years has been Stewart Lee's Comedy Vehicle. Everything back to basics, just one bitter, cynical man and a microphone, complaining about everything for half an hour. His show on books and literature was amazing. Again, I don't know how well it translates.
This is another thing in the comedic 'divide'; much of American pop culture becomes, by osmosis, pop culture elsewhere. We can't go to Taco Bell but we know all about it. The reverse is not true, however; Family Guy can be full of references to other US shows and we'll still get it, but if a UK show is full of references to tons of other UK shows, then it may have trouble translating to other audiences because not all of those shows will 'make it' abroad. This might be able to breed a sort of cultural élitism amongst people who 'get the references' if they watch a lot of UK shows, and keeps up the perception of UK shows being somehow cleverer because they're referring to things that, although mainstream in the UK, seem more niche overseas.
Britain really seemed to have a golden age of comedy that is waning; there haven't been any shows of the quality of, say, Brass Eye or The Day Today for a while now; American comedy shows, as has been mentioned, often seem to outstay their welcome, perhaps due to the pressure of having a hugely successful show, and stopping running it creating a 20-week void in the schedules. Hence even hugely acclaimed shows like Frasier feel like they've done everything they possibly can when they stop. The likes of Curb Your Enthusiasm have stayed fresh (this has been my favourite show in recent times) but then, like the likes of Family Guy and the Simpsons (which is on the downturn these days), these aren't 'conventional' sitcoms; they don't have the inherent clear limitations that the likes of Friends and Roseanne had.