We prefer a larger, heavier bullet on these. In a target-grade rifle, the .308 can be used effectively on steel and paper targets out to 1,000 yards. Normally bullets such as Speer's 168 and 190 grain match boat tail hollow point are used for competition. In most rifles, the .308 is capable of top-notch accuracy. Winchester is a military spn-off, surplus cases are readily available.
Military cases are often thicker than commercial ones, and have less case capacity.
Also, try to match headstamps for more uniform results. One cartridge may be awesome for one application, and only moderate in another area. Do this well, and it will cover up a myriad of other sins. Pick a cartridge that's in the general ballpark of being appropriate for the job, add marksmanship, and the rest will follow.