A few thoughts:
Much of perceived recoil is caused by the sound. There are some huge differences in noise reduction depending on the ear protection. Going through the shop and looking at db ratings, esp. at low frequencies, can be enlightening.
Fast burning powder allows you to use less grains for equivalent shot performance. Powder gas contributes to recoil as exit velocities can be high.
Gas operated semi-auto shotguns kick noticeably less than pumps or doubles, in my experience.
Stock design can also increase/decrease felt recoil. A stock that has a large drop will tend to kick the gun up into the jaw. There are custom stocks available aftermarket that are supposed to reduce felt recoil.
Some say synthetic stocks can reduce recoil since they absorb energy.