Yes, I know, but the shot column exiting the barrels would be the same, no? So, why is one a "cylinder choke" and the other a "light full"?
Why is it that constriction matters more than diameter?
Dr Wanker actually got it pretty much right with his 3 dimensional balls on a pool table analogy... even if that explanation was a bit of an over-simplification.
There are interactions as those little balls, or pellets move down a parallel bore that result in what we call a cylinder bore pattern. The relatively abrupt change when the little balls hit the tapered section we call choke obviously causes the paths of the little balls to become influenced into a tighter pattern as the constriction become greater, within limits. But we also have to factor in a lot of other variables such as the velocity of the little balls, their hardness, roundness, and mass. Then there are still other variables such as shot cup material and thickness, polish of the bore, gas blow-by, number of pellets, i.e., number of collisions, etc. that will introduce pattern variations from using differing loads in the exact same barrel.
Because of the large number of subtle variations, and the unknowns concerning their final influence upon the resulting pattern, I suspect it would still be very difficult to create a computer program that could predict a shotgun pattern with a high degree of precision. It is simple physics. Kind of like understanding and explaining the expansion of the universe, but on a somewhat smaller scale.
Just think, we all may be on our way to God's pattern board!