Lets talk about the two calibers you named here. 338 LM and 300 RUM.
Since you said elk hunt I will say 338 LM and list some reasons why. Sure the 300 RUM is a good elk rifle too but here is what I like better about the 338 LM.
Are you a re-loader? 338 LM has the best brass available by far.
Barrel life will be longer in the 338 LM.
I would assume longer distances are on the menu so the 338 trumps again especially past 1000 yards.
Elk tend to hang in states that can be pretty windy, I will take a 338 on a windy day every time.
Also if you get the 300 RUM you will still want a 338 LM down the road, so why not go for the big dog and be done.
Jeff