My dad's got a Savage .308 and another in .22-250, they're model 110s though. They're excellent rifles, and I'd have absolutely no trouble recommending them. The accutrigger is a really, really nice feature IMO.
He's spent a ridiculous amount of time messing around with them and has the .308 shooting MOA at 500 yards. For what you've mentioned wanting to use it for, I think I'd go 30-06 just for the ability to use heavier bullet weights on elk. The .308 will do the job, but shot placement's a bit critical.
YMMV.
As to larger calibers wrecking more meat, obviously a clean shot is a clean shot. Doesn't matter if you're using a .243 or a .50 BMG. Put one through the ribs broadside, minimal meat spoilage, the critter falls over dead.
Now, my brother in law is using a .300 Win Mag using 180 grain bullets. He took a slightly (max 25 degree) front quartering shot on a mule deer last year. The bullet deflected off the upper leg bone just below the shoulder blade and went back... It exited the opposite corner ham, pretty much obliterating it. Now it's a single anecdote, we can play shoulda coulda woulda all day, but IMHO if it had been a lighter, slightly lower velocity .30 cal like a .308 the damage would've been mitigated, it probably wouldn't have done as much damage at the back and stopped before it exited the body cavity. IMO it magnified the error.
The heavier calibers do give you more versatility in bullet weights for shooting larger stuff though, that can't be argued.
Wiley.
