In the early 1980s I patterned a lot of loads and found following. So called "magnum" shot patterned at least one full choke percentage tighter than "chilled" shot from same maker (Lawerance?), sometimes almost two choke percentages. Going to Cu-plated, magnum shot, from same maker, gave 3-5% tighter patterns at 40 yards than for same shot, unplated. In each of these comparisons, other components of load were same.
One gun was 1973 Browning Citori in 12X76 with nominal full and 1/4 choke constrictions, and loads were in both 70 and 76 mm hulls with one-peice plastic wads. Load weights were 1 1/4 and 1 3/8 oz. Other gun was 20X76 with nominal 1/2 and 1/4 chokes. Load weights were 1 1/8 oz. Both guns would go to high 80% patterns in tighter barrel and 70% or higher with open barrel, with some loads. With other loads, with soft, low quality shot, percentages could be as low as 50% from tight barrels and 30% from open barrels. Shot sizes were nominally #6, #5, #4 and #3 -- actual shot sizes were often "half-sizes, that is, #5,5, #3,5, etc.
On ducks and geese, the Cu-plated shot generally penetrated deeper, apparently because it pulled many fewer feathers into the bird.
Was somewhat surprised when, many years later, I found that Bi-Sn alloy shot, which was/is "ugly" and irregular, patterned as well as the Cu-plated shot in a 16X70 with full and 1/2 chokes and also pulled few feathers into ducks and geese.
Niklas