It's amazing how littlle I've read here about the .375 H&H. It's the classic 'big game' caliber and proven potent enough for all game in Africa. My dream is to SOMEDAY hunt there, but right now, I've got kids to raise.
I think that, truly, the key is shot placement. Toting a .416 or .458 if you aren't competent with it is worse than carrying your '06. If you can't hit the target, the odds of JJHACK having to do the worst part of his job increases.
Here's a thought to stir up trouble. What about a .45-70? Loaded with 500 grain hard cast bullets, it's a penetration machine and the compact lever action allows several rapid follow-up shots without removing the gun from the shoulder. Add a peep sight or 2-5x scope and you've got yourself a game gun, I'd say.
As far as my personal selection for caliber to hunt with. I'd either take a .375 JDJ or .45-70 in a T/C contender or a .454 Casull revolver. Loaded to max, all three are PROVEN on big game and would be very satisfying on a personal level to use.
When the game bites back, though, it might be prudent to carry both...