For 15-20 years or so, I had both: several different versions of .300 magnums, as well as a couple of different .338 mags. During that period, one or both usually went with me to elk camp each year. Without checking my hunting journal, I would guess that I shot about half a dozen bull elk with each caliber during that time period.
I have never shot an elk much beyond 300 yards, and most have been between 100 and 200. If there was discernible difference in terminal performance between the two calibers, I never noticed it. The first bull that I shot with a .338 Win Mag (at about 20 yards) ran just about as far as any of those that I have killed with three different iterations of .300 mags.
When I reached my mid- 60s, I got tired of the recoil from the .338s, and I traded them off. When I turned 75, I gave my last .300 Win Mag to my stepson.
These days, I hunt elk with either a .30-06 or an improved version of the .338-06, and I am already thinking about just using a 6.5 PRC for all my big game hunting.
