Double lung/heart shot, biggest target, safest/surest shot to anchor them. Elk are big strong animals with a huge zest for life when they feel threatened. No two situations ae the same, my son's first bull dropped at the shot (high lung shot), my last bull went maybe 20 yards from a center punch double lung shot (.338 WM). Shoot them through both lungs or the heart, and they won't go very far.
I'll be hunting in an area with plenty of private so may need to anchor it right then & there and head/neck shots are smaller targets than high shoulder.
I've had bang flops with a 257 and had them run like the wind after catching a 375H&H in the same place. If they're keyed up to run when they get tagged, and you don't shut down the computer, they're gonna run.