Unlike others, I have only taken 3 elk - first was perhaps a 250 yard off-hand shot with 308 Win 165 grain bullet - I hit that one too far back - I did get a corner of a lung and tore up the liver - was several hours tracking before I shot that one a second time, in back of its head. Next time that I was in that area for elk, I had a 338 Win Mag - 225 grain bullets - second elk shot at perhaps 100 yards, third one at perhaps 15 feet. Both of those I saw fall down and stay down. Those are the only three elk that I have ever fired at, although I assisted with the recovery of two more - my son used the same 308 Win and killed his with a single hit (we heard him fire four times, but there was only one bullet hole in the carcass); my Dad used two 165 grain rounds from his 30-06 - although either round would have done fine - the bullet holes were maybe 3 inches apart. So based on that, I would say your 150 grain 300 WSM is more than the 308 Win that I used, and less than the 338 Win Mag that I used. But you can kill an elk with it, if you are able to. My guesstimate would be 180 grain or 200 grain would be your preferred bullet weights in that cartridge, for elk. I have no experience, at all, with mono-metal bullets, so I can make no suggestions about them.
After only killing 9 elk, I don't classify myself an an expert elk hunter. Seven out of the nine I killed was with the good ole 30-ought-6. The OP has a 308 win, which would suffice with 150 grains however, having the grand ole ought-6 would be a nice nastalgic choice, other than the 300 WSM.
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