The easiest way to answer your question is to take whichever rifle you shoot the best. If you shoot both equally well, there's only one answer: the 340!
Believe me, you will notice a difference on game hit with the 340.
I wonder how many people that are recommending the 300 have actually owned both.....
I own both a 340 WBY and a 300WBY, and to tell you the truth, the 300 now spends all of it's time in the safe. I really don't have much use for it now.
A 300 Mag is probably the single best all around rifle for North America - if you're only going to own one rifle (God, wouldn't that be awful).
Have you tried the Barnes Triple-Shock X? My 340 doesn't like either the original Barnes X or the XLC, but I tried the Triple-Shock and it loves them. They are a much friendlier X bullet.
I've come up with what I feel is an excellent combo: my 340 for heavy stuff, and my 270WSM for everything else. I shoot 225gr / 140gr respectively; both are within 50fps of each other, and have the same trajectory - only one trajectory to memorize.
Both of your rifles will do an excellent job on an elk, but the 340 will do it better from every angle - that's something to keep in mind on a limited time hunt far from home.
Good luck on your hunt.
Jay