In my humble experience... This varies from hunter to hunter,
@cajunchefray
Some of my hunting peers simply cannot tolerate recoil and would prefer to hunt elephant with a 7x57mm Mauser (like WDM Bell) if it were legal.
Some of them can barely control the recoil of a .375 Holland & Holland Magnum, yet show up at the white hunter's camp with double rifles chambered in calibers as large as .700 Nitro Express due to some misguided insecurity about "Being a real man".
And then, there are some crazed dare devils like myself who are fortunately not troubled too much by recoil. I have hunted a hippopotamus bull on land with a .600 Nitro Express in the past. And also hunted American bison with a .505 Gibbs. The recoil genuinely does not trouble me at all. And I'm no Herculean bodybuilder.
So it really does vary from hunter to hunter.
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 black powder 8 bore and 12 bore rifles with the .600 Nitro Express (or any other big bore rifle) and .375 Holland & Holland Magnums (or any other similar caliber of this class). And the principle is still very much the same.
