Like most things bigger is better and this situation is no different but that statement comes with a caveat.....only go as big as you can shoot accurately! A .338 would work great but if you flinch heavily and therefore can't shoot it accurately this can easily result in chasing a wounded bear through thick bush where a well placed shot from a 30-06 can easily result in a dead bear. Know the capabilities of you, your caliber and the bullet of choice and keep the shot distances within that affective range and you will have a dead bear! Good Luck!