IF you are talking about the "big five" in Africa (Cape Buffalo, elephant, rhino, lion & leopard) if you are the hunter with a PH backing you up, I'd use a .375 like the H&H or Ruger, or a .416 such as the .416 Rigby. For a stopping rifle, nothing under .45 caliber qualifies, and bigger is better, except the leopard does not require an elephant stopper.

For Kodiak, Polar, and big grizzlies, I think the .338 Win. and similar rounds with premium bullets are sufficient, but I'd use my .375 H&H or .416 Rigby for 1000-pound and up bears!

The .30/'06 with heavy premium bullets will kill (and has killed!!) anything on earth with one shot. BUT you must be a superb marksman, AND YOU MUST KNOW YOUR QUARRY'S ANATOMY VERY INTIMATELY, IN ORDER TO KNOW JUST EXACTLY WHERE THE BULLET MUST HIT!! The Inuit kill polar bears with the .22 Hornet and .223 Remington. Jack O'Connor's wife used a .30/'06 to kill her elephant. Bell killed over 800 elephant with a 7X57mm Mauser (275 Rigby).

My recommendation: use the biggest, most powerful rifle you can shoot well. Big bullets don't work if they miss.