I did the Africa thing (plains game/buffalo) with a .375H&H, and had intended to take a .416Rigby along as well, but had last minute problems with the rifle and wound up taking just the one gun. The .375 was just as perfect as you always hear...easy to shoot, accurate, flat-shooting enough for anything reasonable, and deadly...worked on everything.
The thing is, after shooting a .375 for decades on deer, moose, black bear, coyotes, crows, and tin cans, you get accustomed to using what everyone is calling a "big gun"....but it isn't a big gun when you're hunting buffalo. Suddenly you're using just an "adequate" gun, but when you are accustomed to big guns, "adequate" won't cut the mustard...you want BIG!
Sure, a Rigby is "big", depending on your point of reference, but it's expensive to buy the gun, the ammo, the dies, even the components...and it's not that much more gun than the .375.
A .458 (win or Lott) can be bought much more cheaply, can be reloaded cheaply, can be downloaded to .45-70 ballistics easily, and yet can still step in and be a big gun when you want or need it to be. You can shoot it until the cows come home without breaking the bank, and then when the chips are down you will be holding and using a gun with which you are totally familiar and comfortable. Bring on that elephant! Yeah, a double would be even better, especially one in a .458 caliber Nitro cartridge that could use the cheap components for practice...but look at the price tag for the gun! Yikes!...that's a good start on another safari tied up in one rifle!
As Ardent says, don't #### around waiting...make the move and do the hunt, it's easier and more painless than you think...and if you have any romance or sentiment in your soul, do it with a gun that BELONGS in Africa!
And as for the .257Weatherby someone mentioned...is that a rimfire?
John