What would you choose and what bullet for elk?
Either one, with confidence.
My 22� .338WM launches a 225g AB @ 2750fps. A .338 Fed can launch the same bullet well past 2350, but even at that velocity it will retain 1500fpe past 550 yards. Given a 200 yard zero, a 36� drop (roughly the height from brisket to back on a mature animal) gives you a range of 425 yards. Maximum Point Blank Range for a 6� target would be about 240 yards.
By contrast my .280 Rem pushes a 140g AB to 3038fps (26� barrel on a Ruger #1, so same overall length as most rifles with a 24�� barrel). That load retains 1500fpe another 25 yards, to 575. Zeroed for 260 yards, MPBR is about 305 yards and a 36� drop occurs slightly past 525 yards.
If those won�t suffice for 99% of your elk hunting you�re doing something very different than most people.