Your question about theoretical accuracy of the 308 vs 30-06 vs 300wm is well asked and in fact may have more to it then even you know.
The key word here being "theoretical"
Anytime theory and fact disagree, it's easy to figure out which is wrong. But theory is often made into religion by members of the shooting world and facts are ignored.
The truth is as follows (at least in part)
The 30-06 was developed between 1904 and 1906 and was sized to use a case nearly full of the powder needed to achieve the desired velocity with the powders available in 1904. It was fitted to the Springfield m1903 rifle. As time went on the cartridges were loaded with different weights of bullets and also with better powders both by the US Military and also by all civilian manufacturers. It was (and is) a grand old cartridge and still one of the very best all-around shells the world has ever seen. Perhaps the very best.
In the late 40s and early 50s the military load for the 30-06 was loaded with powders that filled the shell only about 85% full and the M2 load (for the M-1 Garand rifle) used a 150 grain flat base bullet. So with the formation of NATO and the idea of a cartridge for all members to use in their rifles so ammo can be shared the idea of using the same diameter bullet as the 30-06 was something US Military leadership was unwilling to give up, and because 80% of the budget for NATO came from the USA, the US Military got it's way. So the new shell (called M65) was reshaped to bring the brass shoulder back to fit the powder charge, and thereby making the cartridge fit into auto-loaders easier and allows for a more compact action with basically the same ballistics as what we had with the M1 Rifle.
Now the new shell was made on more modern machines and the M14 rifles were also more modern and made on machines that were not worn. Such an improvement in manufacture made for a bit tighter tolerances and all US military rifles made for the new 7.62NATO (308) were made this way, so overall the M14s were a bit more accurate then the M1s.
In comparing the 308 Winchester rifles made in the 50s and 60s to the 30-06s, we see comparisons made many times of the best and latest 308 barrels and ammo against some 30-06s that may be of the same quality and same age, but also made against some that were older and somewhat worn, or against guns and barrels made all the way back to 1906. So it's "a given" the average was going to favor the 308 in accuracy.
"Reasons" were often quoted as having to do with short actions being stiffer, but that really has nothing to do with the issue at all. See the accuracy results of various guns used in competition with new barrels since the 60s to the present day and you'll see no direct relationship of groups to action length. Yes, most shooter use the short actions because the short shells use a bit less powder, and so get better bore life, but the advance of the accuracy standard is NOT related directly to the action length as we see by so many good and winning groups shot by those shooting the 300 magnums and some of the 7MM mags over the last 50-60 years.
If the short action was really more ACCURATE we would never see a long action ever win a match again. As we can say that bi-wing prop driven aircraft are not as fast as jet fighters and be 100% correct. You NEVER see an air race with a prop driven bi-plane win against jets. That's something we can say with certainty.
But you cannot say you never see a long action rifle win a match. In fact I can't say that my short action rifles are more accurate then my long action rifles at all. (or less accurate) Accuracy is by far more effected by quality of the barrel and how it's fitted to the action, quality inletting as well as quality of the ammo. The bullet has no idea how long the action was that held it in the magazine ---and "doesn't care".
I do not deny that most of the best accuracy we see today is being shown to us with rifles made on short actions, but not all. And because it's not all I think we can safely say the action length is used for other reasons but really has nothing o do with accuracy per se.
So if the quality of 3 barrels and the workmanship of each rifle, and the quality of all 3 cartridges were equal, I would say there is no real difference in accuracy between a 308, a 30-06 or a 300 mag.
I think the biggest reason the 30-06 is not used in competition much these days is more simple.
The 308 does all the 30-06 will do and gives better barrel life using bullets up to 168 grains. The 30-06 does beat the 308 with heavier bullets but the difference is small enough that if a 30 cal shooter wants more then the 308 gives him, he usually jumps over the 30-06 and goes straight to one of the 300 magnums. It's about speed--- which reduces fight time.
But not intrinsic accuracy.
