I have used both and they are both great options. Personally I like the ATI better. It just fits my hands better. I swapped the original butt pad out for an AR style Limbsaver and that made a HUGE difference. Be advised however that accessin the Slide Release Lever is a bit tricky with the pistol grip stocks. (If your interested I make extended levers for this reason.) If anyone you know has one or the other ask them to go to the range with you and try it out. Understand, however, that while the Knoxx Recoil Reduction actuates on a spring/slide system to "reduce" the felt recoil, the ATI doesn't move. It has a nice sized rubber pad at the palm swell area on the pistol grip to absorb and allow better control. Some have stated that if not held correctly the Knoxx will have a slight "jump" up and can inadvertently slap you in the cheek area.
I think I covered everything I can sum up, but, if I think of anything else to add, I'll be back.