I think the pattern board does not tell the whole story.  Even when loaded with the same shot load I prefer the 12.  The increased diameter makes for a shorter shot load and a shorter shot string in flight.  Not as important when shooting at a stationary target but makes a big difference when pass shooting at moving targets.  I also think the shorter shot column and larger choke diameter means less pellet deformation with lead shot anyway, making it easier to find a good load/choke combo in the 12.