I will give you only my opinion based on my little bit of hunting in Africa, however I have reloaded for all of my hunting rifles for a number of years. The minimum required caliber for buffalo and elephant is .375 (or 9.3mm I believe but not 100% sure), so anything .375 and larger are suitable for DG. I'm sure others will have better opinions and knowledge than I do. But in my opinion, it's all about how comfortable you are with whatever caliber you choose. Bigger caliber and bullet, won't make up for perfect shot placement. However, the larger caliber rifles with more ballistic energy might give you a little advantage on a not so prefect shot placement with a possible knock down allowing a quick follow up shot. Now, as far as 458 Win compared to 375 H&H, you can fire a 500g bullet out of the 458, where as the 375 will only be up to 350g. The 458 is probably better known as the closer range (100 yards or less) caliber for larger and DG animals. The 375 can be good shooting out to 200 - 250 yards effectively on animals, however I wouldn't recommend that on any DG animal. And the 458 Lott is the same bullet as the 458 Win but has a larger casing which will allow more powder, more ft-lb of energy, and indeed more recoil. Sorry to be so long winded, but to sum it all up, for many decades DG animals were taken with the 375 H&H, but the 458 has become more and more popular of the years, especially the Lott. So whatever you decide, the most important is what you are most comfortable with, what you can confidently hit your target off-hand, off sticks continuously and quickly. Good luck and maybe others will have a better insight if I've done nothing but confuse you.
