I'm a lefty and have a right hand Beretta 390 and a Benelli SBE in left hand. Doesn't make a difference.... still can't hit anything :grin:.
Seriously, the only difference is that you won't have shells flying across your face but that has never made any difference to me (but it could be a distraction for others). A bolt action rifle is the only firearm that I have found a preference for in a left hand action. Even then, I still occasionally use a Remchester 700 in righthand.
I would make sure you are properly fitted for the current shotgun(s) before changing to a left hand action. Unless, of course, you are bothered by the ejected shells - then you would likely see some improvement.