I have a Knoxx stock but it is not the Axiom, it is the regular one, the Compstock
BLACKHAWK! Rifle CompStock - BLACKHAWK!
It is on my 375 Ruger. I don't particularly like muzzle brakes and so I built a heavy hunting rifle off a Winchester 70 long action. With a #5 Pac-Nor 3 groove at 24", 6x42 IOR Tactical and the Knoxx Compstock it weighs 11.5#. It is not unpleasant to shoot at all and I would compare it to an unbraked 338 win mag. When shooting a 270 gr bullet at 2900 fps then that is not bad at all.
My Knoxx stock is very well made with a full bedding block
But, the receiver and SCOPE come backward and if you are putting it on a heavy kicker then you need to get a scope with the most eye relief you can find. The 6x42 IOR I have advertised a 4" eye relief and it is MINIMAL for my 375. I can feel the scope just touch my eyebrow on a few occasions. I am now thinking about a Bushnell 1.25x8x32 Elite 6500 which has an advertised eye relief of 6". I would assume you would have the same problem if you put it on a long range 338.