No gun throws an evenly distributed pattern, say, like the holes on pegboard. All shot patterns are distributed according to the Rayleigh distribution (akin to a normal distribution). The rate at which the distribution blooms and withers is controlled by choke effect. If the two patterns have the same number of pellets within the 30" circle, it is very likely they have the same distribution. If so, then you have to say they have the same pattern performance. On the other hand, shot string is third dimension of the pellet swarm and can't be seen by capturing a typical pattern. It would be only just slightly incorrect to expect exactly identical performance between two equal patterns where one has a longer string. I know of no definitive data comparing 12 bore to 20 bore for loads of identical power (shot weight and MV).