None of the above.......
Another case of American Magnumitis. You don't need either for the large game you mention and either is too big for smaller game. Even more so if you are hunting in areas with even a small population base. There are lots of calibers including the ones you mentioned that will kill everything dead but the idea of shooting fox and coyotes on a regular basis with those 2 boggles my mind. There aren't any calibers that are "good" for the range in critter size you are talking. Personally, I wouldn't go any bigger than 7mm-08 and I'd seriously look at the 6.5's and rounds like the 250 Savage and the .257 Bob.
LK
Not sure about the "magnumitis", since the .308 doesn't quite qualify, but I agree with you for the most part. I've never needed a .30 caliber anything in the lower 48 states.
But, when we get down to using the minimum cartridge for animals like elk, smaller isn't better for the average shooter. A magnum won't give the average shooter any advantage unless they can place a bullet beyond 350-400 yards, and many truly can't, contrary to popular belief.
And I don't mean that in any way as derogatory towards anyone's abilities, good or bad.
But...
The medium level .30 caliber cartridges give the average guy what he needs to make the shot count. They'll give good penetration on a variety of shot angles, and will kill animals pretty cleanly on any decent shot.
The smaller calibers will also do the job, but as they get smaller, the shots need more "precision", and the shooter needs more patience and "dicipline" to wait for the right shot. Nothing against them, but I've learned the hard way that many shooters are simply "unable" to do that under pressure in the field. I have a best friend/hunting buddy who's much that way, although he's learning as time goes by. He uses a .308 Win, and does well with it, but I doubt he'd do as well on larger critters with a lesser cartridge. He's simply unwilling and/or unable to have the right frame of mind under pressure, so if there's an animal in range he's very likely to shoot at it at the first opportunity.
He's just as capable as anyone of making a shot, but he won't "wait" for a better shot angle.
I'm the other way; I can sit there and watch an animal that's in range without any trouble at all. I'm very confidant in my shooting ability (at both running and standing animals), so when an animal is in range I just watch it 'till the right shot angle is presented.
From a voice of experience; smaller cartridges are not usually the best choice for the average or new shooter. Neither are the big magnums for the most part. I see the smaller cartriges as a good choice for the experienced shooter, but those capable of using it well won't need to ask which one is best to decide what they want or need. The magnums are similar; those capable of utilizing the additional effective range while also being capable of handling the extra recoil won't need to ask which one to choose. They'll have already shot enough long(er) range targets enough to know for themselves what they want and/or need.
So, in my mind that leaves us with the medium capacity cartridges from perhaps 7mm through .30 caliber or so as good recommendations. They'll do the job well in the hands of most shooters, and they're not a bad choice even for the experienced, since they'll do the job just as well for them.
But for general all around shooting of big game, the .308 and 30-06 are pretty hard to beat when it comes to recommending a cartridge for the purpose.
And that from someone who's never owned either, but is familiar with the results they produce.
Daryl