The .308 is enough bullet to take down an Elk... The .308 and the .30-06 are ballistically similar and the 06 has been the go to round for multiple sportsmen to take down large game animals, human beings, and any other assortment of living things. The military as well as police snipers use the .308 for the stopping power... Not that a human being is anywhere similar to an Elk but that should give some sort of nod to the power the .308 has....
Ultimately what matters is the shot placement...
You can never shoot a magnum caliber for the increased power to make up for decreased/poor shot placement!

Good luck on drawing a tag, may your aim stay true, and the heard bull present a broadside shot in your comfort zone!