The 338 Win Mag is a fine round for Brown bears and some use it for Elk,
My self I would rather have a 9.3X62 which is almost a ballistic twin to a 35 Whelen AI... And son, its not how fast a bullet goes butits how it functions at a given velocity.....Thats why deem big ole slow bullets penetrate like no tomorrow....and PENETRATION is the first step to a clean kill..not speed...

And unless you are planning to shoot a Bull elk at 300 yd.'s would be served well with a 35 Whelen or a 9.3X62 or a 358 Win. or a 350 Rem. mag...
or dare say a 30-06 or a handloaded 8X57 or a 308 Winny...375 win.,356 win 444 Marlin or the new 308 Marlin or a 45/70 within 200 yd.s ...but a fellow may have to hunt and be skilled to get closer than 300yd.s
They will get the job done