Since you're focusing on the bigger game and since Caribou and elk can offer long shots I'd be leaning to the .300 Magnum.....however it's edge over the other two isn't truly a big one.

One more thing to consider....the .30-06 is available in lighter guns than the magnums and I find them easier to handle.....this isn't a big deal on a horseback hunt but caribou can be a lot of walking and stalking.