[catnthehat]

Well, I may as well weigh into this one.
between the two, in MY neck of the woods, the 300 is a better rig, for a few reasons.
cartridge selection off the shelf
recoil

Those are two factors most people will have to look at , because many who will buy these rifles do not reload, and cartridge selection should be a priority, as should be recoil.

The 338 typically uses heavier bullets better than the lighter ones, whereas the 300 shoots very well with 180's or even 165's.

I have loaded and shot many of both in the past , and although I can shoot the 338's well, the 300's I shot were a lot easier to accurize.

I helped zero a 300 WSM Remington for a fella this fall, one of the new Boone and Crockett models .
it shot the 165 factory ammo superbly, recoil was very light of a 300 , even throwing the lighter weight bullets, and it zeroed at 200 meters with three rounds.

The fella later shot a cow up north with it, and his partner shot one with a 300 mag browning with hand loaded 180 grain ammo that I had made for him.
Both rifles shoot well, and both are happy with their choices.
That being said, neither rifle would be my choice to hunt with , and I would not look at the 338 either simply because i don't need them and cannot shoot either for more than one shot without my shoulder injury re occurring.

FWIW, I know many people who have done Africa and Alaska with 300's and never had a problem with them dropping animals.

Cat