Answer:
The difference is mainly the British's exaggerated use of sarcasm. American humor is more gentle and mild where the British humor is crude and in most cases rather mean.
I wouldn't say that American humour is mild, at all. From what I have seen in films and on T.V. it uses physical comedy more than English humor does. English humour is sarcastic, but isn't crude or mean in most circumstances, it seems more cleverly worded humour.