As already correctly mentioned, I recommend the 338 cal magnums for hunting elk at ranges over 1000 yards. Is it a requirement, certainly not but the larger caliber and heavier bullets will help get you out of a pinch in the event of a shot placement that lands on the fringes of the vitals.
I do not know your specific situation but most that I talk with that want a deer and elk rifle for long range shooting generally hunt deer MUCH more often then elk. For deer at ranges even out to 1200 yards, you do not need a 338 cal magnum but it also does not hurt either but there are other options such as the 7-338 Lapua, 7mm AM, 30-338 Lapua, 30-338 Lapua Improved or 300 AX.
Any of these will easily kill any bull elk on the planet out to 1200 yards if you put the bullet in the right place.
Another advantage of the 338 bore however is barrel life. it will offer a longer throat love then the 7mm or 30 cal wildcats on the Lapua case.
As far as which 338 would be best for elk at long range, hard to say because at these ranges any 338 magnum from the 338 RUM up to the 338 AX or 338 Kahn are all very much up to the challange.
Decision comes down to if you want the option to shoot factory ammo or if your alright to pay for fireforming cases. As mentioned, the 338 Lapua is extremely accurate, very powerful and no fireforming needed.
The improved versions of the 338 Lapua offer more velocity, up to 150 fps more which with a 300 gr bullet weight, very significant. All in all, take your pick. Have the built properly and all of them will make you very happy with the end results.