Solitary Man has pretty much said it all. IMO, a properly-aimed 7mm Rem. Mag. will do anything a .300 Win. Mag will do, with a little less recoil. Of the cartridges you mentioned, the only time I would opt for the .338 instead of the 7 Mag. is if I were certain to encounter Alaskan coastal or Kodiak Island brown bear or polar bear where they are legal game.

In addition to N. A. game, the 7 Mag. is adequate for all non-dangerous African plainsgame and everything in Europe.

The .338 has noticeably more recoil that the others mentioned. However, sinceyou consider a .300 Magnum to have "light" recoil, you will not be bothered by the .338.