I'd say the distinguishing difference between the British and American version is the British tendency to understate whereas American comedies tend to exaggerate the characters (this is a generalisation of course). Brits are generally given to defer to authority whereas American culture is much more oriented towards independence.

Another series worth watching is 'The Thick of It' and also "Yes Prime Minister'. We have a tradition of mocking characters who are elevated beyond their level of expertise or intelligence rather than challenging authority per se.

I'm not rating the 2 styles - I enjoy and appreciate both while there are terrible British and American comedies alike. It's an interesting take on how comedy and satire translate into the national psyche.