What's different is the affect, and the acting. And its a significant difference. I like Steve Carrell and the US Office is amusing, but its forgettable 5 minutes after the show. Its mindless amusement.
The british show had an edge - that is the difference. The humor cuts deep. That kind of humor doesn't play in America. So they softened the show and the characters - extensively. THe US Office is a watered down version of the original.