Some of the old guys, Greener thought an 8 bore was about right and that a smoothbore was adequately accurate for the 40 yard shot. He thought the .450 Nitro was OK, too; but you had to be sure your Nitro express is built right to stand the strain. They were still learning about containing smokeless pressures. He said if you were shooting a .303 on safari, take two because they are not as durable.
John "Pondoro" Taylor, an admitted ivory poacher, added an extra category, the medium bore in the .40s, adding that the .375 H&H performed as well as the .450-400, the previous all around rifle. He thought the .577 was best for "fighting elephants in the bush" with higher velocity and better bullet shape than the .600.
Walter Dalrymple Maitland Bell was famous for killing elephants with small bores. He liked the .256 (6.5 Mannlicher) until he got a bad lot of ammo and went to the .275 Rigby aka 7mm Mauser. I saw at a gun show once, a .275 of his, with a letter to Rigby, concerned that their promotion of the High Velocity 140 grain semi-spitzer might lead them to a slower rifling twist than his standard 175 gr full patch called for. I don't think it did; both loads are listed in my 1939 catalog. He eventually went to the .318 Rigby and was heard to say late in life that the then-new .308 Winchester would be a good gun if given proper bullets.
He owned one or another big bore express rifle, but you don't hear much about it among the small bore publicity.
But, he was a good shot, knew the anatomy, and was hunting naive game that did not know to fear a white man with a rifle.
Lots of pukka sahibs tried to emulate him with less success and got stomped, gored, or clawed.