My vote would probably go to the 7mm-08 even though the .243 ammo would be a little more universally available. It is light on the recoil and yet with a good 140gr is adequate for elk.
The .243 is a very popular deer gun (yes, even in the west) and would probably rank in the top 10 calibers when talking deer taken. However, because of it's weight limitations (105gr is about max available), ranges should be kept under 300 yards for reliable kills.
On another note, I believe you can get "managed recoil" loads for the .308 and the caliber is probably the most inherently accurate of the bunch. It can also be loaded with (standard) bullets ranging in weights from 110gr up through 200gr with excellent results. It is actually ballistically superior to the .30-06 in bullet weights of 165gr or less. There is a reason the military snipers use it for their light weight sniper guns.