Ruger 308 varmint/target.
Out of the box with hand loads, it would hover around .80MOA. Factory loads will be around 1 MOA.
The receiver glassed in will get you down to .60 MOA, but the barrel heats up pretty fast, so don't try to push long strings.
The ammo cases need to be blown out, or you get too much blow-by to get you under 1 moa (read factory ammo). The factory chambers are bit loose (standard reamed), with a long throat, so blow the cases out before you start working up loads. And, get a single round sled so you can load one round at a time by hand. The bullet (tips) will need to be set out a bit longer in order to just kiss the lands of the rifling, which may not load into the well.
As for full blown, Re-barred (29") with bolt trued and lapped, receiver squared, glassed, trigger worked, and 36x scope, mine will hold .30 all day long with groups in the .20 range on the average.
Out of the box, it will hold it's own with the 700 VSSF/PSS, but when it comes time to smith (upgrade), the REM is going to be the cheaper option.