I learned to shoot at long range with a .30/06 M-17 Enfield sporter, topped with a 3-9X40 hunting scope. There wasn't enough vertical adjustment in my scope for long range shooting, so often I would have to set a sighting target on top of the backstop, which was often an esker with an impact target below it. Incidentally, I shot very respectable groups at long range with that rifle, sometimes well in excess of 1000 yards, although it would often take several rounds to get the range worked out. Shooting over wetlands makes spotting your own shots pretty easy as you have time to recover from the recoil and reacquire your sight picture.
When I finally had a long range rig built, I chose the .308, because I had a short action to build on rather than any preference for the .308 over the '06. In fact my original plan was to get a 40XB in .30/06, but opted for a custom job instead. I am of the opinion that a greater effect on accuracy occurs from the choice of components that make up the rifle, and how those components are crafted into a rifle, than there is from the choice of chambering the .308 or .30/06. So many knowledgeable people are of the opinion that the .308 is more accurate than the .30/06 that I am hesitant to argue the point, but I question whether one can make use of the difference.