Do realize that the Saiga shotguns used in multigun and tactical shotgun matches are all uniformly relegated to the realm of Open Division shooters at nearly any match. Tactical/Limited divisions are the domain of semi-auto tube fed shotguns, and pump guns rule the roost in He-Man/Heavy Metal division.
I've handled some of the converted Saigas, including the Red Devil gun featured in the video linked above. The guns point and handle nicely in much the same manner that an M1 Abrams tank handles nicely for a vehicle that weighs in excess of forty tons. For multigun Open Division shooters, the Saigas are a uniquely-engineered game changer, but certainly not without their limitations. However, since the vast majority of targets at these matches are static and ground-based, thre ability to repeatedly engage aerial targets with a perfect degree of repeatability is not nearly as important as it would be for a trap, skeet, or sporting clays competitor.
Open Division Saigas are a niche tool modified to fill a particular role. This is no different than a Perazzi trap gun built to fill an equally particular niche of an entirely different sort. You can't really equate one with another, and claiming a Saiga is just as good for trap or bird hunting as a custom-fitted over and under is just as ridiculous as claiming that a Perazzi would be a fine choice for multigun.
Some people can't tell the difference, but this does not mean that no difference exists.