Big animals and big cartridges.... they are just kind of made for each other.
I wouldmake the 300WinMag in the B.A.R. my#1 choice. Use 180 gr. premium bullets (like Partitions) and never look back; figuring you handle both guns reasonably well. I know folks get sentimental about their 257 Wby's however....
Check out the "Poll: Elk Cartridge Preference" thread. It poses this question,
"What is your
current favorite elk cartridge that you personally have actually used to take elk?"
One can't help but see the preference for heavier hardware by those who actually do the elk hunting AND actually harvest elk. Plus we are constantly seeingthe smallbore fanswithin our group move from the lighter duty stuff to the heavier duty stuff for elk.I think the numbers in the pollspeak louder than much of the verbage you are about to recieve. [Actions talk and BS walks.]

BTW, absolutely take your 257 along as a back up rifle (your #2). Elk hunting is rigorous and crap happens --- broken stocks, damaged scopes, etc. (ever see a horse decide to voluntarily roll on the ground with a rifle still in the scabbard? ANY time it is a big time hunting trip, alwaystake a spare rifle. Personally, I'd prefer a 30-06 as a minimum for my back up rifle for elk, but that is me.