ST Graves is right about the .308/7.62X51. The Army adopted it and it became the standard service round in 1957 and they began work on a match grade round to replace the M1C and D sniping rifles, which weren't particularly accurate not due to the round but due to the platform. The M21 was developed for the Army and the Marines had the M40 developed through Remington, using their 40X action. Carlos Hathcock actually used a Model 70 Winchester in 30-06, though.
The problem with the 30-06 round wasn't that it was inaccurate. It was that it wasn't accurate enough with the powders used in WWII. The round was loaded with IMR4895 or IMR3031, and it didn't fill the case enough. That couldn't be changed either, because the M1 Garand was timed for these powders, and when Mr. Hodgden and DuPont came out with the slower burning 4350 and 4831 classes of powders that were ideal for the -06, they couldn't be used in the M1 due to pressure issues at the gas port, which accelerated the bolt and op rod too rapidly, bending op rods periodically.
The .308, however, was ideally suited for powders in the burn range of IMR4895, which gave a 90 to 95% fill in that casing. This meant that the burn rate was more uniform in the .308/7.62 when it was developed because its case capacity matched the powder. So the M21 was much more accurate than the M1D. When you load the -06 with the newer powders which give a good fill to the cartridge, it greatly increases its velocity, burn rate uniformity and accuracy. In my Hodgden powder reloading book, StaBall 6.5 and Superformance will push the 180 grain Sierra at 2850fps or so from a 24 inch barrel at maximum charges. 165 grain bullets with these powders are up around 2970 to 3000fps.