The main reason that the 308 is so widely used for bench rest competition is it's inherent accuracy, low recoil extreme efficiency for the 308 bore and less but very important low muzzle flash characteristics.
These attributes are why the round is used so widely for Sniper missions. It's great accuracy is capable of 1,000 + meter shots.
The 30-06 based rounds are over bore capacity, create massive muzzle flash and due to the incomplete powder burn in the bore, create a very loud secondary report, giving away the position of the shooter. This fact also depletes accuracy as well. This is why this round is not preferred as a Sniper round. Also because the 30-06 round only betters the 308 by 100-150 fps so very little trajectory advantage is gained as a result.
For shots over 1000 meters, the Long Action Rem. 700 in 300 Win Mag. are used, (M-24A2) based on the same basic rifle platform as the 308, only a heavier barrel is used. (A #6 taper or larger)
For our beginner who started this thread, he would do much better with the easy shooting characteristics of the 308. (7.62 NATO) Because of the vast availability of ammo and components, bench loading this round is by far the best choice.