The .338 would be the better of the 3 for large bears and moose, but both the .300 win mag and .30-06 will take all as well, with the .300 win mag being "superior" to the .30-06. I am biased, but if your looking for the best flexability, long range capability, flatter trajectory and good comprise of power and not overwhelming recoil, then the .300 win mag would be the best overall choice.