There will always be folks who claim the .30-06 is a more accurate cartridge.
The 30-06 cartridge itself is more capable from a physics standpoint than the .308. Period. In turn, the .308 is more capable from a physics standpoint than smaller caliber cartridges. Period. This has been written about extensively by many knowledgable authors. It has been heavily studied and well understood for about 100 years.
... and then there are caveats...
Assuming the barrels are all equally constrained by how much pressure the alloys can contain to spit out the bullet as fast as they can, the shooter is by far the most inaccurate part of the system. One of the things that the 30-06 requires in order to beat out the .308 is a higher BC bullet, via higher mass (all other aspects being equal). The same can be argued about the .308 vs smaller calibers. To make heavier mass, higher BC bullets fly introduces more reactive physics, which necessarily either pushes the limits of the rules of competition (muzzle brakes, rifle weight, etc), or higher cost (bigger mechanisms cost more and so does practice ammo and other things), or induces higher recoil on the shooter, which invites flinch. All three of those are human issues, not cartridge issues. The 30-06 doesn't care about competition rules or cost or how much recoil is on the shooter's shoulder. In physical terms, it will always beat the .308 if given a big enough bullet and high enough charge. And again, the same applies to .308 vs smaller calibers.
Most top highpower shooters feel the main reason the .308 is much more accurate than the .30-06 is its shorter, fatter case promotes more uniform and gentle push on the bullet due to a higher loading density (less air space) and a more easily uniformly ignitable powder charge.
There is a lot of touchy-feely bullshit in every person who argues a caliber is inherently better than another because "gentle push". The actual reason is because the shooter is "uncomfortable".
All I have to say to them is to properly test .308 vs. .30-06 and find out. Theory is nice to think about;
I will at least agree with this.
facts determine the truth.
I disagree that what some selection of shooters are better able to shoot with is a fact for other shooters. Physics is physics, and that is factual. However, shooting skill and physical abilities and the size of your bank account heavily influence opinions on which caliber is better, and those opinions do not count as "facts".