The 30.06 Spr. is probably the most versatile as it gets. This cartridge will handle a wide range of bullet weights from about 110 gr. to 220 gr. For a few ears I used only the 30.06 Spr. for critters from coyotes to feral hogs to mule deer. I cannot imagine it not being suitable for elk, moose or black bear if the bullets are well chosen and the shot done right. But I have zero experience with elk, moose or bear.

If I were to have one and only one, and choosing between the two you mentioned .. 30.06 Spr.