As a former high volume clay shooter - the reason we use OUs is:
1) We hate cleaning shotguns therefore avoid autos
2) In Sporting Clays, it can be advantage to have two different chokes vs compromising two different target presentations
3) OUs are inherently more expensive therefore we can show off more
4) The weight and length of OUs (we were shooting 32 inch barrels in my day) assisted with swinging the shotgun (not stopping when trigger pulled)
5) OUs break less than autos (the normal "most reliable" autos of that time were Beretta 390s and 391s with the Rem 1100s and Browning Golds (my favorite!) were "bring a spare"