With the proper rifle and proper skill, .308 would be OK for Elk.
And let's be real here: You need a proper rifle for elk hunting (that'll also be OK for other stuff). Must have enough oomph for elk hunting.
.300 Win Mag would be more betterer. Still plenty ubiquitous. Plenty of rifles in that caliber. Still plenty of horse power @ 500 yards.
And easily enough HP to take care of anything else, too.
308 and the 6.5 Creedmore are basically identical ballistics wise until 600 yards
308 and the 6.5 Creedmore are basically identical ballistics wise until 600 yards then the 6.5 Creedmore takes over. That's why I stayed with the 308 Winchester because I'm not going to be shooting anything at 600 yards. When I say ballistics wise I'm talking match grade ammo for both cartridges.
I practice on a 500 yard range I can hit a 12" AR500 diamond so I'm confident I can take game animals out to 500 yards.