The British makers had a rule of thumb concerning recoil to the effect that the gun should weigh 96 times the weight of the shot. Following this rule a gun intended for one ounce of shot should weight exactly six pounds.

A 12 gauge for driven bird shooting will be intended to use a 2-1/2 inch cartridge loaded with 7/8 of an ounce of shot. If it weighs 6-1/4 pounds its over the rule of thumb weight and should not produce excessive recoil.

Over loading a gun results in poor patterning and wastes much of the extra shot. It has to be overweight to keep recoil within reason. That's where we are here in the US with 12 gauge loads in a 20 and 10 gauge loads in a 12.

I don't think the grip has any effect on perceived recoil. The amount of drop has a major effect on perceived recoil. Height of comb will also have an effect but I think the amount of drop has the largest effect.

You will note the trend in modern military rifles is to greatly reduce the drop, in some cases all the way to zero.

It's to be admitted that one expects to fire a gun more than a rifle, but on the other hand, flinch probably affects the results more with a rifle since you are aiming rather than pointing and firing during the swing.