in general terms, if you are getting beat up from a shotgun, you're not shouldering it properly.
if you fire the gun with the stock not firmly held against your shoulder, you will get a kick from the acceleration of the gun caused by the equal and opposite energy imparted to the shot load and gun.
if you hold the gun tightly against your shoulder, the perceived recoil will be less. it will have the same energy, but will be spread over a longer period of time.
recoil pads add little mass to the gun to reduce perceived recoil and the "sponge" of the recoil pad is too slow to effectively pad or dissipate recoil energy. but, it does help you if you shoulder the gun properly because it will form fit to you as you pull the gun into your shoulder. this couples the recoil energy to your body mass more effectively, and that is what reduces the perceived recoil !
sg