Different barrel, completely different deal. It all depends on the shotgun (actually the barrel) and the load as to how it will pattern, and there's no way to predict it short of patterning it.
At 15' (5 yards) I expect patterns not much bigger than bore diameter from the shotguns and buckshot loads I use. Of course, I like tight patterns, and have over the years found barrels and loads that produce those type patterns for me. The shotgun closest at hand right now is a 12 ga. 870 with an 18" 870 Police barrel, marked as CYL, which will print about 4" patterns at 25 yards (75') with its preferred load of 00 buck (Federal LE 127 00 with FliteControl).
Whatever pattern size you want is what you should go after - these days it's reasonably easy (compared to a few years ago) to achieve the pattern size you want at reasonable ranges. Often enough with a 12 ga. it's possible to do just by experimenting with different buckshot loads, unfortunately the variety of 20 ga. buckshot loads is not as wide, so that ability is more limited - at least at present.