After many years of wanting a .300 Weatherby, a few years ago I finally built one (Vanguard). I only shoot handloads, and my .300 Wby likes both 168 and 180 gr TSX bullets, and shoots 3-shot sub moa groups with each. So far I've only used this rifle on two hunts (3 Texas exotics and a Montana elk), and all were one shot kills with the 168 gr TSX handloads. The elk was a 5 point bull that when the bullet hit him, he turned, took two steps and fell dead. The shot was about 100 yds hitting him tight behind one shoulder, went through both lungs, and exited behind his other shoulder.
168 gr TSX, R-P cases, 78.5 grs IMR 4350, CCI 250 primers, 3290 fps
180 gr TSX, R-P cases, 84.0 grs IMR 7828, CCI 250 primers, 3191 fps
This July, I'll be taking this .300 Wby and my 168 gr TSX loads to South Africa to hunt Sable, Warthog, Klipspringer, and some other small antelope. Although this TSX load did not make large exit wounds in any of the animals that I have shot with it, I'm developing a load with Hornady 150 gr FMJ bullets to minimize cape damage.
Like others have written, a good elk load will work fine for African plains game. Shot placement and familiarization with your rifle are more important than caliber or type of bullet. The 180 gr Nosler Partition has a long record of being a top performing bullet on both North American and African game animals.