I think the point is that the smaller the gauge the higher the chamber pressure is.
To me this would explain why a 12 gauge 6 1/4 lb. gun shooting a 3/4 oz. of shot has less felt recoil and less pressure as a 28 gauge weighing the same amount shooting the same load.
Neither of the two formulas relate to felt or actual recoil forces they simply explain why two shot charges of the same weight require higher chamber pressures to achieve the same velocity. Check out a few loading books and compare the difference in chamber pressure for loads fired in larger bores as compared to the same charge weight fired in smaller bores and it will become quite evident.
