.300 win mag will easily do the job. I assume you are shooting at a decent distance? 500+ yards?
I use a .308 and drop pigs and deer like its my job.I would use it for elk as well.
.338 cartridge isn't cheap but I would love to own a .338
This year I am hunting pigs with a spear.rifle just doesn't do it for me anymore. I am going to work my way down to knife.
Once you master knife, go for strangulation. Then go for making them so depressed they kill themselves walking off cliffs.