Generally speaking, and infusing sixty years of shotgunning, info from WW Greener's book, and other inputs, the same shot charge from an equivalent constriction through different size bores will pattern better from the larger bore. In other words, an ounce of shot from a 12 will usually have a more even pattern than an ounce of the same shot from a 20, chokes being the same. Main influence is the longer shot string "rubbing" the bore in the smaller gauge. Lots of other things influence patterns including the forcing cone length, kind of wad, hardness of shot, style of choke and probably a dozen other things. Greener made a shotgun barrel with straight bore, no forcing cone, then used a thin walled case and oversize wads. Fantastic patterns and that was before the days of hot cups. 410 shotguns are notorious for blown patterns with the heavier charges of lead shot. The standard trap load for the 10 gauge was the same 1 1/8 ounce in 1900 as it is for the 12 today. Patterns weren't thinner. BTW, patterns are generally the %age of the payloads total pellets in a 30" circle at 40 yards regardless of gaugev(excepting 410). I've fired hundreds of them.
