ddress00,
The .308 Winchester cartridge is enigma. It's also one of the best cartridges for all North American game. Lots of Rocky Mountain hunters use it.
After climbing all over the Rockies carrying a heavy rifle, I began to understand utility of a lightweight rifle. So I bought one. But before I did, I did a lot of research. Initially I was going to go with a .280 Rem or an '06. I was surprised by what I had learned. The .308 Win is an efficient cartridge. It is an inherently accurate cartridge. It is a powerful cartridge. And it's a short-action cartridge. To my way of looking at big game hunting, that combo is hard to beat.
Hunters will campfire banter about merits of their favorite cartridges and why they're better killers than other cartridges. Emotionalism does not defeat knowledge. When using practical, western .308 caliber hunting bullets of 180 grains & less, there is virtually no difference of impact velocities between the deservedly venerated '06 and the .308 Win.
I can go on forever about the merits of the .308 Win, but I'll just post velocities I've chrono'd out of my 22" barreled, bolt action .308 Win with factory ammo:
1. Hornady 165 grain Light Magnum: 2900+ FPS
2. Federal Classic 150 grain: 2900+ FPS
3. R-P 150 grain Core-Lokt: 2900+ FPS
4. Federal Premium 165 grain 2700+ FPS
6. R-P 180 grain Core-Lokt 2700+ FPS
I do not recall any ammo shooting above MOA.
While I've never shot an elk with my .308 Win, I wouldn't hesitate to do so. The .308 Win will destroy any elk's heart and/or lungs just as surely as any other cartridge. And I do know from my own experience that mule deer will die when hit with a .308 Win bullet. I would not hesitate to hunt elk with a .308 Win.
The .308 Win in a lightweight rifle will not bruise a hunter's shoulder. Its accuracy instills confidence. After carrying heavy rifles for far too long, one grows to appreciate a short-action, lightweight, powerful rifle.
BTW, I've recently read an article that indicated that the .308 Win has passed the '06 in popularity. The '06 needs no accolades from me. It has done everything on the North American continent and others.
To answer your question: were I limited to one .308 Win bullet it would be the Hornady 165 grain Light Magnum. Right on its heels would be the R-P 180 Core-Lokt.
My hunting experiences have taught me that the dominant criteria of success are hunters' skills in finding game, maneuvering into position for advantageous shots (A bad shot is a bad shot regardless of cartridge.) and accuracy skills. Any suitable cartridge will kill. No animal can live sans heart and/or lungs. The adage that a .243 Win to heart and/or lungs is a whole lot better than an '06 to the guts is right on target, so to write. And we certainly cannot lose sight of the fact that our hunting forefathers killed all North American big game with surplus 7x57 & .303 British rifles. So it ain't cartridges alone that kill. Hunters' skills at putting bullets where they need to be factor heavily in the game-killing equation.
Next elk season I ought to be in one of Utah's premier trophy elk units. I will use my .270 Win as my primary rifle. And I will take my .308 Win as its back-up. I am trusting what might be a once-in-a-lifetime trophy elk hunt to these two cartridges. That's how respectful I am at them.