30-06 fires a heavier bullet at a higher velocity...
308 fires a lighter bullet at slower velocity......
so if a 308 is more accurate than a 30-06 does that mean a 22lr is more accurate than a 50bmg????
they are different calibers in the same high quality gun barrels and actions....
My experience is that my 30-06 has no problem nailing clay pidgeons at 200+ yards and neither does my friends 308.....and we also have shot 600yds with same results
we both know our guns and i also know that the faster heavier bullet at the same range will generally cause more damage
so accuracy seems more up to you than some other factors when considering vary'ing calibers of such close power....
i think 308 is only more popular due to the military's view of being able to carry more ammo with less weight