A .308 will kill an elk at 500,600 even 800 yards if you do your part. As will any of the other rounds mentioned. The limitation is mainly in the shooters ability.
In that ^^ post I am in no way advocating shooting an elk at 800 yards with anything. I am merely stating that arbitrary functional kill distances for a given caliber are pretty much false. People form opinions on the “max” range for a given caliber using rumor and conjecture AKA gun writers, hunting magazines and campfire talk.
It really depends on the equipment (optics, bullet/load, accuracy, and ability of the shooter) much more than the chosen caliber. It also drastically depends on your style of hunting and the local conditions.
If you are primarily hunting in open country something with some reach and optics on it is your better choice. If you are hunting in tight dark timber something else might be a better choice.
I tend to hunt in both types of terrain and it’s why I like a .338 or a .375H&H with a good controlled expansion bullet and a low power variable scope. It covers those quick snap shots at less than optimum shot angles in the thick stuff and it gives you some reach in the open as well.
That being said I killed my last bull about a month ago with a .308 shooting 165 Gr Nosler Accubonds at 524 yards. That bullet exited and put him straight down. Would a 7MM or a .300 or even a hot rod .338 have done any better? Not in this circumstance, no. Dead is dead, full penetration with expansion is full penetration.
We are blessed with excellent bullets, accurate and dependable rifles and unbelievably repeatable and precise optics now days. If you utilize and train with the technology available now days you can pull off shots that would have been unthinkable not that long ago and with calibers that you wouldn’t consider adequate even a decade ago.
BTW I am not recommending going out and buying a .338 or a .375. I’m just telling you what I’ve been using for years with good success for my style of hunting.
A hunter should know their limitations and not take shots that are beyond their training ability. If you’ve never shot anything at 400+ yards in your life. Doing so on a snowy, windy day at a living animal in the field is a really bad idea. Caliber, scope, bullet will not make up for a lack of in the field shooting, practice and knowledge. If you’re having to guess at hold over at range on a calm day off a perfect rest, you’re pissing in the wind, don’t take that shot.
I can bang a 10” steel plate at 600 yards all day long from improvised field positions and rests. Until you add some gusty and variable winds, then it gets a lot more dicey. But you’ve got to put in the trigger time to know that.