I really like this quote from Sir Samuel White Baker in “Wild Beasts & Their Ways”:
“There can be little doubt that a man should not be overweighted, but that every person should be armed in proportion to his physical strength. If he is too light for a very heavy rifle he must select a smaller bore; if he is afraid of a No. 8 with 14 drams, he must be content with a No. 12 and 10 drams, but although he may be successful with the lighter weapon, he must not expect the performance will equal that of the superior power.”
And George P. Sanderson In “13 Years Amongst The Wild Beasts of India”:
“I advocate the use of the heaviest rifle the sportsman can manage upon all sorts of game. Yet it is not unusual to hear men express a decided opinion to the contrary, generally conveyed in the formula, "A small bore is big enough for anything." Such men should rather say, " I cannot carry a heavy gun," or, " I cannot shoot with one," than speak against them on principle.“
Even though both of these authors are from the 19th century, their assessment is still very much on point today. Just replace their blackpowder 8 bore and 12 bore rifles with .505 Gibbs (or any other big bore rifle) and .375 Holland & Holland Magnums (or the 9.3x62mm Mauser). And the principe is still very much the same.
The .375 Holland & Holland Magnum’s biggest advantage is that it has a very manageable recoil and a very flat trajectory. It’s penetration (assuming the right bullets are used) is perfectly adequate for the sort of shots at dangerous game which a client hunter will be needing to make. Knock down power is absolutely of no consequence to the client hunter, since it’s the white hunter who will be the one to normally deal with a potential charge or escaping game. For most visiting hunters on African safaris, they typically do all of their domestic hunting with some form of .30 caliber (such as the .30-06 Springfield or the .300 Winchester Magnum) and don’t have the experience to comfortably shoot a large bore rifle accurately. The .375 Holland & Holland Magnum and the 9.3x62mm Mauser are two calibers that really shine in this department. It’s very easy for the average client hunter to be able to shoot one accurately with very little practice.
I’ve personally been shooting 4 out of Africa’s Big 5 (Elephant, Cape buffalo, hippopotamus, lion) ever since 1974 with .375 Holland & Holland Magnum rifles over the years with successful results.
But I would not have the same level of confidence in this caliber if I was not being backed up by my white hunter (who invariably carries a heavier rifle). As a matter of fact, I did once almost lose a gigantic bull elephant which I shot 6 times in the heart-lung region with a .375 Holland & Holland Magnum and 300Gr Remington round nosed steel jacketed FMJ solids.
If I were ever to (hypothetically) hunt dangerous game without a white hunter present, then I would opt for some type of .500 caliber (such as the .505 Gibbs or the .500 Jeffery or the .500 A Square or the .500 Nitro Express). If elephant was not on the menu, then I would contend myself with some type of .450 caliber (such as the .450 Rigby or the .458 Lott or the .450 Nitro Express).
Since white hunters invariably shoot at dangerous game under unfavorable circumstances (such as having to shoot charging or departing game or having to follow up wounded dangerous game in areas with dense foliage and low visibility), the additional knock down power of the big bore is indispensable to them because they can’t afford to be picky with their shots (unlike a client hunter).
To conclude, bigger is definitely better but only if the operator can properly manage the recoil and shoot the rifle accurately. Otherwise, the big bore becomes counterproductive. A 600Gr solid bullet from a properly loaded .505 Gibbs will down an elephant quicker with a heart-lung shot than the same shot being taken on the same elephant with a 300Gr solid bullet from a properly loaded .375 Holland & Holland Magnum (assuming of course, that all other factors are equal). But in order to do that, the operator must be capable of firing the .505 Gibbs accurately and comfortably in the first place… something which comparatively few client hunters can do compared with those who are accurate shots with the .375 Holland & Holland Magnum.