Many of the Spanish, Italian and British guns had a "pigeon model" that was meant for the heavy duty use at pigeon matches where loads were hot and heavy and a lot of money was riding on the outcome. These guns were typically 1/2 to 1 pound heavier than target guns and up to two pounds heavier than their standard field gun.
Some still use the term "pigeon" today (most notably Beretta), but those guns are not currently built to that spec.
AyA still makes a few models meant for heavy-duty use that I know about. Most folks don't use SxS for most of those purposes any more, unfortunately. I just got my S&W Elite in today - a nicely built 20 gauge that will be for birds - carried a lot, not shot as much. For heavy use, I use my Brownings (until I can convince Zippy to part with one of his P-guns for a mere pittance). My guns are target guns, meant to go the distance. Some are better than others, which is why P guns, K guns and similar cost what they do - pure, rugged simplicity with tolerances NASA would envy and reliability that Toyota would crave.
In short, if you're looking for a serious, high-round count shotgun for lots of targets, an O/U is most likely going to be your best bet. If you can find an older SxS that was meant for trap, pigeons, etc., you might have lucked out.
Now that I know that I, as a LH, can shoot DT's with no issues, my search is on for a nice 12 gauge SxS.........
And the quest continues................
