When the 300 Win Mag was developed, the 308 Norma was fairly well established and Winchester could have simply chambered for the Norma and everyone would have been happy. They might have done so except for a couple of things. Obviously, they wanted their own cartridge with the Winchester name. Also, the 308 Norma was loaded HOT! I suspect the pressures generated by the Norma factory loads at the time were a bit higher than Winchester engineers were comfortable with.
The obvious thing for Winchester to have done would have been to produce the 30/338. They would have then had four cartridges based on the same brass and would have had a cartridge which fit the pre-64 Model 70 nicely. The problem was, the 308 Norma was, as I mentioned, already well established. The marketing people at Winchester felt that, in order to compete with the Norma, their cartridge had to be physically larger so it would, at least, have the appearance of greater power. Winchester ads emphasized this size advantage and this may well have played a part in the success of the Winchester offering. In truth, ready availability of ammunition probably played as large a part. A 300 Winchester based on 338 brass would probably have fared well in the marketplace just due to the availability issue but I don't doubt that, in this instance, size mattered.
Some may have noticed that the 308 Norma case is actually slightly longer than the 358 Norma and may have wondered why. The reason was to ensure that the 308 Norma reamer would clean up a 30/06 chamber.
In the mid-seventies, Norma thinned the web of the brass to add capacity to the 7x61 S&H brass and this carried over to the 308 Norma so later 308 Brass will have a thinner web and sidewalls. At about this same time, pressures were reduced somewhat (the pressure reduction might have resulted from the increase in capacity but I suspect the powder charge might have been backed off a bit as well) and so was velocity.
Some may find it interesting to compare dimensions between the 308 Norma and the old 30 Newton. I have long theorized, had Winchester chambered the Model 54 (and later, the Model 70)for the Newton cartridges, we would never have seen the 308 Norma or the 300 Winchester. In fact, we would probably have never seen any of the standard magnum cartridges and the 300 H&H would have stayed in England. GD