While I have never put an aftermarket pad on a shotgun, I have both pre-fit and grind to fit LimbSaver and Pachmyer Decelerator pads on many of my rifles.
Between the two, the LimbSaver is my preferred choice for the harder recoiling rifles/larger cartridge combinations.
Some were more to extend the lop of the firearm than to improve felt recoil reduction. The other benefit, is that compared to hard plastic or metal butt pads, the rubber butt pad keeps the rifle from slipping and falling when standing in the corner or leaned against the wall.
I do like the Pachmyer Decelerator with the hard insert at the top of the pad, for my lever actions. This is known as the Sporting Clays model... it is designed to keep the softer rubber from catching on your clothing as you mount the firearm quickly. Does work.