German Salazar's article on the .30-06 vs .308 is a good one. But it only compares one rifle in each caliber and one shooter doing the tests.
When the .308's scores in competition trumped virtually all the .30-06 scores in the mid 1960's, its 30 to 40 percent better accuracy was attributed to one little difference that few people nowadays know about. With equal quality rifles, barrels, cases, primers, powder and bullets, the best .30-06 match rifles back then shot about 5 to 6 inches at 600 yards properly tested. The .308's shot about 3 to 4 inches at its beginning. The reason was primarily attributed to the 2.5 degree leade angle on .30-06 chambers being too steep. .308's had a 1.5 degree leade angle and bullets were less deformed as they entered the rifling. A .30-06 with a 1.5 degree leade angle shot more accurate.
At all ranges and both cartridge chambers having a 1.5 degree leade angle, the difference is small nowadays, but enough to show that .308's shoot better scores at 1000 yards than the .30-06. I think Sierra tried using the .30-06 to test their 30 caliber bullets 180 grains and lighter but it never quite equalled the accuracy the .308 produced. The track record of each at the Nationals and other NRA high power matches prove this. The .308's case is more condusive to lower muzzle velocity and pressure curve spreads; a critical element of good accuracy. Most folks won't tell the difference. Back when both rounds were legal in Palma matches in the USA, the .30-06 shot some really good scores but was never king of the mountain. One factor's the .308 moves the rifle less in barrel-time recoil than the .30-06 and that makes it easier to shoot accurately.
Afield in hunting rifles and with bullets 180 grains and lighter, it'll be hard to tell the difference. With heavier bullets, of course the larger case capacity of the '06 makes it a better choice. But few animals can tell the difference between two bullets smacking into them with only 150 fps difference in impact speed.
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the 30-06 is an awesome round . much better than a 308. if you had competed Against German you would say the same thing. the 30-06 stays super sonic to 1000 yards without loading to red line pressures.