Haven’t watched either in ages (and only seen bits of the US one), but from memory the UK one was quite subtle in how the mockumentary format worked, and how the characters interacted with the camera, while the US one eventually bludgeoned that and every character spun to face the camera every time anyone said or did anything (which then led to Parks and Rec doing that to an exponentially higher degree again).
Everyone knows that Operation Good Guys was the real pioneer of a UK sitcom in that territory anyway.