It's quite the even match in my books. British comedy can be either hilarious or just awkward and unfunny.
A good example (which I might want to put the old flameshield on for) would be The (original) Office, which I was persuaded by a co-worker to watch because it was "funny and better than the American version". I didn't like it. I got it, I knew what the tone they were going for was, but it just didn't really hit me. The American version did.
I could go on but if I did I'd be here forever. Both sides have their strenghts and weaknesses, funny people and outright talentless hacks who have no business near a comedy club. For me, at least, it's a tie.
Being from Finland I might add that our comedy is usually only funny when Swedish people are involved.