Diyj, While the .308 cartridge design itself is inherently more prone to accuracy than the .30-06, there are a great deal of other aspects important to target shooting...for example, the .308 fits in a short action, so your lock up will be more solid, it's much more shootable from a recoil standpoint, I can shoot 100 .308rnds before I get as sore as I would from 50 .30-06's, and it's cheaper to shoot since it uses less powder (brass is usually cheaper too, for some reason, I would assume just a volume of sale thing). The military switched to the .308 because it's every bit of the killing power of the .30-06, but with less overall weight and powder consumption.

If you're considering moose or big bruins, or basically anything that might dictate that you use 180-220grn bullets, the .30-06 is the choice, it handles heavier bullets better than the .308. Up to 165-180grns, they're pretty evenly matched, but beyond that, the .30-06 starts to pull away, until anything over 220grns at which point either of them turn to crap (shot a box of 300grn .30-06's one time, TERRIBLE!).

Personally, I don't think you could go wrong with either, I've got three of each in the safe right now, guess I REALLY couldn't make up my mind. (No two are really alike: .308's=Ruger compact, M-1A, and Remington 700PSS, .30-06's=M-1Garand, Ruger standard M77 and Ruger No.1, I've also got my fiance's .308 M98 customized/sporterized Spanish/German Mauser, I'm glad she lets me shoot it whenever I want!!!)