Rainer,
To think the 308 is not inherently more accurate than the 30/06 is fine but illustrates a lack of knowledge as to what the real accuracy capability of the two cartridges is.
It is entirely possible, even reasonable, to build a 308 which is capable of .2 moa accuracy or better. This not at long range, of course, because the shooters are not capable of producing this level of accuracy at long range.
I have nevr seen a 30/06 which was capable of much better than .5 moa. I do think it should be possible to make a 30/06 which would manage 3/8 but I think 1/4 would be absolutely unattainable. Keep in mind, a 1/4 moa rifle is not one which fired a 1/4 moa group one evening in May two years ago. It is one which can be reasonably expected to produce a group of 1/4 moa or better any time the conditions permit. Also, such accuracy does not discount flyers!
So, at these levels, the 308 is definitely more accurate than the 30/06.
At long range, where superb accuracy is more on the order of 3/4 moa, the 30/06 can manage but at a cost. The velocity is significantly greater than that of the 308 (on the order of 150-200fps) but this increased velocity is not enough to make up for a 1/4 moa (or more) accuracy deficit.
Now, in all fairness, the 308 is also less accurate when loaded to work at 1000 yards. It is not all that common to see accuracy at much better than 3/4 moa when using bullets and loads required to make it to 1000 yds. Nonetheless, I have always been able to achieve significantly better accuracy with 190 -200 grain bullets in the 308 than in the 30-06. In one case, this was tested with the same barrel on the same action and stock. The barrel was initially in 30/06 then was set back and rechambered to 308.
As I have stated before, recoil, even if it doesn't hurt you, can cause you to lose a point now and then just because it penalizes you for a poor hold or follow through. The effects of greater recoil are insidious and often the effect is a surprise but it is there nonetheless.
As much as I like the 30/06 as a cartridge, I won't be trying it again at long range. To be perfectly honest, except where it's use is mandated I won't use the 308 either! Regards, Bill.