FWIW,
I had several rifles chambered for each as well as the 300 Roy. Not one of your choices, but I am partial to the 300 H&H.
Just Sayin!
GWB
This all day. ^^^^^
Early on when the 300 Win was newish (1960's) the recoil was as bad or sharper then the 338 Mag. The 338 was more of a push and not as sharp as the 300 Win. I went with the 338.
As far as 300 WSM, well the new SM are just a sales pitch. Can't see the need for the new Short Mags, other then desire for something different. And that is just fine.
The 300 WSM and the 300 Mag don't do much more than the 30-06 or the 300 H&H already do, maybe a few more yards for the same drop.