Why the differences?
Shooting off the right shoulder with a straight left arm might not be too much of a disadvantage for a game shooter taking nothing but straight overhead driven birds, as long as the stock is on the shortish side.
However, the same grip on a Sporting course where you shoot at a huge number of differently angled targets is a definite handicap because it restricts gun mount and movement.
Bending the elbow by bringing the hand back a little on the fore-end brings a heck of a lot more gun movement on the bird. Try it.