I regularly attend mid range matches and shoot either a 223 Space Gun or a 308 Win match rifle. The local mid range matches are held at 600 yards. Six hundred yards is a long way for any shooter, but both the 30-06 and 308 Win are supersonic at that range. There is a F Class category called tactical, which is the 223 and 308 Win round, I seldom shoot 1000 yards, but the 308Win is the most popular 1000 yard tactical round. The 308 Win is at its extreme range at 1000 yards, the typical round drops below subsonic. I have shot 168's at 1000 yards and the things tumble when they go subsonic. The 175's stay stable. I have shot 190 SMK's and they stay stable. Currently the 155 Palma and the 185 Berger are the most popular 308 Win bullet at 1000 yards, the 155 Palma guys have to push the thing above 3000 fps, and they do that with 30" barrels.
The 30-06 is probably a better 1000 yard round than the 308 Win as you can push the round 150 fps faster than a 308 Win. At 600 yards there is little between the two, the 308 Win has less recoil, both are more than acceptably accurate out to 600 yards.
Having pulled targets for new shooters, I can say 300 yards is a long way for people who don't practice each weekend. If you ever shoot on paper you will find that just hitting the target at these extreme ranges is an accomplishment. Rock busting gives one an erroneous idea of accuracy, as you really don't know where the bullet landed, but you get a reaction on the ground. Once you have to put the bullet on paper, you see that consistency is hard to achieve and hitting what you are aiming at is not a gimmie.