Bingo!
If you shoot bullets of 150 grs or lighter, the .308 has the advantage, particularly when chambered in a short action rifle. As bullet length and weight increases, the advantage of the .308 diminishes, at 180 grs the '06 proves superior in rifles with equal barrel lengths, and when loaded with bullets in excess of 200 grs, the .308 is completely outclassed, unless you lug around a rifle with 30" of barrel, and have the chamber throat cut long so you can seat the bullet so as not to intrude in the powder capacity of the short case. I have a fast twist .308 like that, it makes nearly 2700 fps with a 210 gr VLD, but it weighs 20 pounds when equipped with scope, sling, and bi-pod.
IMHO, the .308 sporting rifle is at it's best in a carbine length, mountain rifle configuration. Light to mid weight bullets have sufficient velocity to produce pleasingly flat trajectories, and their terminal performance is prudent for the medium sized game. Conversely, the .30/06 is at it's best with a 22"-24" barrel, and will tend to weigh in the 7-8 pound range. Combining long, heavy for caliber bullets with a high density propellant means that a long bullet can be seated without diminishing the powder capacity of the long case, resulting in terminal performance suitable for game heavier than is usually considered typical for a moderate .30 caliber rifle. This certainly is substance over fluff, but the advantage is lost on the typical Canadian hunter who views a moose as heavy game.
The advantage of the .30/06 is lost to the .300 magnums, and the advantage of the .308 is lost to the 7.62X39 chambered mini-Mauser. But either cartridge has sufficient overlap to provide suitable performance across a wide range of big game hunting scenarios, and that is the light in which each should be considered.