Like others have posted, your .308 Win (and .50 cal ML) will handle any of the animals that you mentioned, IF you use the right bullet and put it in the right place, from a reasonable range.
Caribou are smaller that elk, and, at least the ones that I've seen, are not hard to kill.
For North American game, a .308 Win would not be my first choice for coastal Alaskan brown bears, but a .308 Win shooting a 180 gr bullet has more energy at 100 yds than either a .460 S&W shooting a 300 gr bullet or a .500 S&W shooting a 500 gr bullet at 50 yds, and all three of these cartridges have killed these big bears.
I just bought a .308 Win but mainly for ringing steel at our range. My .308 used about half as much powder as my .300 Weatherby, and it rings the steel gongs just about as loud as the .300 B does.