a few more logs to throw on the fire.
Does short action matter to you? If a short action is important, if you like the idea of having to pull the bolt back 1/2 inch less theirfor making it a tiny bit faster, and the overall length of the gun a little less, then of the three 308 is the answer (and then we got to talk about 7mm-08)
If not, cross 308 off your list. 30-06 covers EVERYTHING the 308 does, and then does some more.
So now we get to 270 vs 30-06. This is pitting Elmer Keith vs Jack O'Conner. It is Coke vs Pepsi, Blondes vs Redheads, Black Lingerie vs Red Lingerie...wow, I better stop before I get myself too excited....
<whew>
Okay, as everyone said, .270 or .30-06 will do you just fine. They are nearly identical. Truth is, in ability they overlap greatly, but not completely.
30-06 is a little bit better with the heaviest loads. This means the 30-06 is a little bit better for elk and moose, (and grizzly I suppose, but that is stretching it).
.270 is a little bit better as far as fast flat shooting. This means the .270 is going to be a little bit better for pronghorn, big horn sheep, (and coyote too but that is kinda streching it)
The 30-06 has probably got more margin for a handloader to ring out enhanced performance, and truely there are more variety of 30 cal bullets to set on top of it than any other diameter in the world.
but on the other hand .270s recoil a bit less, making it easier to shoot accurately.
So, on your den wall, aside from deer what looks better, more exotic, which would you be a bit more proud of, a Moosehead or a Bighorn Sheep?
If you said moose, go 30-06, it will cover you for a lifetime for whitetail, muledeer, and elk, and still work for that one hunt you eventually set up to go after moose. If you said Bighorn sheep, get the 270, it will cover you for a lifetime for whitetail, muledeer, and elk, and still work for that one hunt you will eventually set up to go after Bighorn Sheep
Also, I have heard it said that the 270 has got a reputation for accuracy, so manufacturers always pay a bit more attention to 270 rifles than they do to their similar breatheren, as they know they will be scrutinized, and any defects will be blamed on the gun, not on 'inherently less accurate round you got in their buddy' That story could well be bunk, but I'll share it.