While either will kill an elk, I would use the one that has the best chance to put an elk down quickly. I have had elk run down into some awful places after they were well hit, and getting them up and out of those places was backbreaking. If you are hunting the sage flats or open parks it may not matter much, but if there is a steep draw full of blowdowns nearby it can matter a great deal. Carrying a light rifle is great while you are hiking but the heavier rifle will be more steady when you are either (or both) in the wind and winded.
The .300 Win Mag with a heavy bullet would be my choice.