I've taken a number of deer with my .243 and while the caribou are slightly larger in size than your average Whitetail the .243 should be sufficient and it doesn't kick bad.
Like the other poster said, if you use this caliber beef up the load and get a good bullet in there i shoot Nosler partitions in mine and rarely does a round go in the paper without touching a previous hole.
I currently use a .338 ultra Mag. which is overkill for the Boo, but comes in handy if I come across a big grizzly. I have a custom muzzle break on there that brings the kick down to .270 range.