Personally, if this were one of your only guns i would go with the .308.. it can probably hunt more than the 7mm-08.

4feathers:
I own a Browning Lever Action 7.mm-08 that I purchased for my wife to use because it is light weight, easy to carry, shoots straight and doesn't kick........ unfortunately, she has never used it. The reason: I USE IT! I love that little rifle for deer hunting here in the woods of northern Moinnesota. It is a joy to hunt with and I'm not planning to part with it for any reason. There are six empty cases in my one and only box of 7mm-08 shells = six deer have hit the ground! I have loaded up some Sierra 160 gr. Grand Slam bullets and they perform extremely well up to 250 yards. I have no doubt they will drop an elk, if and when I get that chance. - ThreeThumbs

I've had the same question. My reloading manual show that you can stoke the .308 a bit more, so I decided to go with it because of the greater flexibility (and because you can often get military ammo cheaper).