There's not a lot in it in terms of performance when comparing factory ammo. The WSM uses less powder and has a more efficient case design, sure - but it's also loaded to higher pressure and that's mostly what closes the gap against the 300WM (If you ever do start reloading, 300WM has plenty of untapped potential horsepower there - plus there's better brass available).
On paper, recoil energy is similar. Recoil of the WSM is meant to be a bit snappier as it uses faster powders in a shorter fatter column, at higher pressure - the WM, using slower powders, a taller case, and lower pressure, produces more of a heave. Both will still kick the shit out of you unbraked or unsuppressed and you'd be hard pressed to tell them apart. Rifle weight and how linear the recoil is, makes a larger difference to felt recoil.
Depending on the rifle model, there's little to no difference in action weight and length e.g. Tikka's are all the same. If the manufacturer produces different length actions, yeah there might a small saving. We're talking a few ounces and perhaps an inch though.
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