I don't think an experienced gun-fighter should be slightly better than the average person in a gun fight. He should stand head and shoulders above the average person in a gun fight. He just shouldn't do it by shrugging off gun shots.Warhammer 40K has a great system that is mimicked very well in the Pathfinder Ultimate Combat system Wounds and Vigor. It makes your average adventurer slightly more powerful than the regular commoner, but then what is all that experience really good for if it's not going to make you slightly better than the average person?
If you didn't know how D&D worked, but you knew that a 4th-level character was supposed to be a hero, you wouldn't immediately define him as able to take four times as many bullets, +20% accuracy, etc.
He would be awesome by almost always hitting, even while shooting blindingly fast and getting shot at. Ordinary city-slickers might have a 1-in-20 chance of hitting, while he'd have a 19-in 20 chance of hitting.