Third Rock from the Sun was incredibly funny, at least in the first few seasons, in the end it wasn't that great anymore, but it wasn't that bad as, say, Friends, which was funny for the first couple of seasons and then gradually became unbearable. Third Rock is one of my fave US sitcoms, after Frasier and Arrested Development. If we count adult cartoons, then obviously I would count The Simpsons until 8th or 9th season or whichever it was, South Park at its best, and Archer. And of course Seinfeld, though I was never a big fan.
On the other hand, Brits have had brilliant TV comedies ranging from Only Fools and Horses to Monty Python's Flyng Circus to The Office (although the US version is OK, too, the British original is the first in my heart).
The brits have put out duds for sure. I think there are a number of strengths they have that we don't.
1. Not afraid to use senior actors/actresses as leading characters (Waiting For God, As Time Goes By, Keeping Up Appearances), which tends to remove barriers of having to look good in every shot (Friends, and the equivalents thereof).
2. They've been able to pull off some Sci-Fi comedies (Red Dwarf, HHGTTG, and yes, I would include Doctor Who). The closest we've done that I can think of is Third Rock From The Sun, which I have a strange hunch was not that funny ( I never really watched it).
3. A show not designated as a comedy can be very funny (Doctor Who, Rumpole Of The Bailey).
4. The ability to pull off historical themes. The brits were able to produce a successful renaissance era comedy (The Black Adder). We haven't produced any comedy westerns, or pilgrim/founding father comedies. I have to admit though, that the Brits attempted another Renaissance era comedy that was a flop.
5. I don't think we have anything like Monty Python's Flying Circus.
I would agree with most of these, however, 3) is also true of some American shows. Buffy, anyone? (Angel, Firefly, too, occasionally.) US TV is quite fond of dramedies.