Hmmmm, depends on the meaning of "greatest." I'll assume you meant most versatile, and by that standard, I think the .30-40 is it.

Being rimmed, it works in most of the classic actions. It's modest standard pressure allows it to work in modern replicas of some of the medium strength actions, such as the rolling blocks; but loaded up, it has enough case to beat the .308, a cartridge well respected for big game hunting. It's long neck and throat allow use of high sectional density bullets (ie. 220 gn), of which there is an excellent selection for it's bore size, including solids.

If the hunting of dangerous game is the figure of greatness, then the .375 Flanged Mag. would be the obvious choice. If the hunting of the meanest and most dangerous game is desired, the .450 NE is the classic.

An aside: I feel an underappreciated case is the .33 WCF. The parent .45-70 brass is available around much of the world, it uses standard .338 bullets, and there is enough case to (when loaded up) make for a magnificent hunting round. The 300 gn Woodleighs (talk about SD!) should go 2150 at pressures around 48,000 CUP, and the 250 gn jobs should go 2350. It could act as a rimmed .318.

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On thinking it over again, "greatest" can easily imply "most used" as much as "most versatile" or "most practical." In that case, the .303 and the 9.3x74R would be the "greatest."