OP,
The .308 is just the 30-06 case shortened down to use faster burning powders. They both do the same velocity with max pressures when you use the same bullets. There is not really much difference here.
If you buy off the shelf ammo then the 30-06 might take it since its been said even the farthest north out fitters keep some instock just in case a hunter needs some ammo's.
308 is said to have less recoil and then their is the mill surp ammo for cheap practice ammo. It is shorter so you get to chose between lighter guns.
It should work better from shorter barrels because of the faster burning powder the .308 uses. 30-06 is stuck using Long cut which is the slowest burning thing out there. The .300 win mag was designed to take Long cut powder when it was state of the art powder.
Now things have progressed and we have new better powders and subsequently the short mag's.
Take your pick. Personally I would take the .308 because I like auto loader rifles and it just shines in auto loaders until you look at the .300 WSM.
That is my 2 cents, thanks for lookin!