It is not acceptable practice to use semi-autos on driven pheasant or partridge in the UK. Mainly because the other guns will be at a serious disadvantage, ( the costs for the day are shared out amongst the guns.)
The argument about not firing the third barrel at a bird, if one has missed the first two shots doesn't really hold water, as there are not many birds that will still be in range for the third barrel !
I use the Beretta 'Eureka' for wood pigeon, where one can quite often fire off up to 300/400 hundred shots in a days shooting over decoys. The shooting is a lot quicker, and the reduced recoil makes a substantial difference.
I also use it for Duck, Goose and Rabbit shooting.
I use the O/U for formal driven days, and rough shooting over the Spaniels.
M.