Hi Otis,
As you have seen I own one of the ATI fixed length pistol grip stocks on a Mossberg 835 and I also own one of the ATI AKITA stocks on a Mossberg 500.
A lot of people like the KNOXX and other recoil absorbing stocks but to me they are butt ugly with their springs, slides and metal tubes. They do absorb some recoil but at the cost of increased danger of a scope hitting your face if you use a scope. The whole gun from receiver to muzzle travels backwards on the spring.
The fixed length pistol grip stock fit the 835 easily as well as the factory stock. It fits the 835 without using any adapter, but comes with adapters to fit other manufacturer's guns. Works well and the pistol grip gives very good control over 3.5" shells. The pistol grip in your hand absorbs a surprising amount of recoil also. There are two issues with it though. I had to use a couple of extra washers as spacers on the stock bolt to keep it from screwing too far into the receiver and effecting the safety action. It also covers the rear of the trigger group making it necessary to loosen the stock to take the trigger group out of the gun.
The AKITA is a really sweet design allowing you to set the length of pull as well as the height of the cheek rest of the stock. I originally bought it for the wife so the gun could be shortened for her and lengthened for me with the push of a button. Works very well and on our 500 with a 20 inch barrel it makes a really compact system when shortened. Not the control that a pistol grip gives you but the surface is grippy and feels good in the hand.