My best guess is the increased muzzle velocity also causes proportionate recoil velocity, and that's what creates the painful bite. My .338 is more of a heavy push (which mathematically might be heavier than the .300's numbers), but is spread out over enough milliseconds to not hurt, while the .300Win gets recoils so quickly that my body takes a full hit rather than recoiling with the rifle.
I was just reading
The Hunter's Guide to Accurate Shooting by Wayne Van Zwoll last night and he addresses this situation directly.
From
The Hunter's Guide to Accurate Shooting:
Felt recoil can vary significantly among rifles delivering the same recoil in foot-pounds ... Slap is my homespun term for what happens during quick recoil. Plainly put, a bullet that exits fast dumps all its energy fast, too. The rifle seems to slap you instead of shoving you. Pile enough foot-pounds behind that slap, and it becomes a punch.
So a better comparison would be to drive those bullets at the same velocity. Some might say drive bullets of equal weight, and I suppose that's one way to do it, but the .308 180 vs a .338 225 have very similar sectional densities, which I think makes for a better comparison. I don't see any load data where the 225 gr bullet in.338 Win Mag can be driven as fast as your .300 Win Mag. Perhaps a better comparison for the recoil would be with the .340 Weatherby or .338 RUM, or download the .300 to the same velocity and then decide. Of course, the rifles and their weights you have on hand are still different which mucks things up a bit.
