With a 308 you have interesting bullet choices when you are talking 1,000 yard shooting.
Bart B. might back me up when it comes to the 155gr Palma or "Fullbore" (depending on which country you happen to be in at the time) bullets at long distance. Yes they are typically launched hot, around 2,950 to 3,050 fps from long barreled 308s, but they are very accurate to 1,000 yards.
Recently an AMU shooter cleaned a 1,000 yard High Power target using Berger 185's, a very impressive accomplishment (his team mates using the same load did not score nearly as well).
For years the Sierra 168gr Match King bullet was the king of accuracy from 300 to 600 meters. It was originally designed for 300 meter Olympic Free Rifle, and it was the bullet used to take the Gold medal back from the Russians after they showed such dominance in the 50's. The 13 degree boat tail did it no favors in the transonic range and it proved unsuitable for shots 800 to 1000 meters.
Berger recently released a 168gr VLD Hybrid bullet with a very impressive BC and shallow boat tail design that makes it a competitive choice for long distance, as it has a higher BC than the 175gr SMK, and can be driven faster.
Still, in the end, any suitable bullet WILL GET YOU TO 1K. The particular BC of the bullet doesn't matter so much as whether or not it is accurate at the distance you plan to shoot.
So pick the maximum distance you want to shoot. Then pick a bullet that will get there accurately. Between two bullets being used for target work BC doesn't mean much as long as they are both accurate at the distance you are shooting.
Since you are just starting out in distance rifle work, get a whole bunch of bullets, all one brand and model, do a load workup (you've been working with the OCW method), and once you get a load that shoots sub-MOA you should start shooting at distance.
Jimro