I've been a .338-06 user for 20 years and although I don't have any experience shooting any of the game you listed I have taken numerous elk from cows to mature bulls and a mature Shiras bull moose with my .338-06. My load has been a 210 Nosler Partition over 56 grs. of 4064 for a chronographed velocity of 2810 fps out of my 24" barrelled pre-64 Model 70 Winchester. All have been one shot kills but one and in retrospect the second shot wasn't needed on that cow elk. The .338-06 is a great medium bore and with proper bullets should handle any of the game you listed. But as with any cartridge proper shot placement along with a good bullet make for a successful harvest.