Robie

Haven't used a .338/06 but all the game you listed can be well taken with a .30-06, so a .338/06 will only do it better. After my first safari where I used a .30-06 I decided to upsize a little, but would still not hesitate to take a .30-06 again. A big 8mm or a .338 to me is pretty ideal.

One of the all time classic cartridges of Africa was the .318 Westley Richards. The main loading was a 250 gr RN-FMJ or a RN-SP. If you have a rifle in that calibre today the easiest way to make up ammo is to open up .30-06 brass to .330 calibre, so it is really not that different from the .338/06.

Except for nostalgia a .338/06 is a better choice in the modern world as there are so many bullets in the 160 gr to 250 gr (and upt to 300 gr ?) range to choose from.