Perhaps a definition of a general purpose rifle is in order. When it comes to killing game from squirrels to cape buff, my .375 is the rifle I reach for. To me that pretty covers general purpose, but in a non-magnum the .30-06 is my choice without hesitation.
While I have no quarrel with the ballistics of the .303, I believe that the LE is at a disadvantage if MOA accuracy is part of the equation, although I have seen a couple that could manage it, and a P-14 can be as accurate and easy to scope as any modern sporter.
The thing about the .308 is this, if you choose it because it approaches .30-06 ballistics, why not just get an '06?
The debate over which is more accurate short action or long has no merit when considering hunting rifles. It has little merit when considering target rifles either, otherwise large caliber long range rifles would of never seen the light of day if they were not accurate.
The .270, .280, and .284 are all proven performers, and would be the cartridges expected to be chosen by those whose experience has been in open country. IMHO, they do not make the cut as general purpose cartridges because they lack heavy bullets. The .30-06 does not lack a fine selection of heavy bullets, yet the '06 will match the sub .30's trajectory when loaded with the appropriate, high BC bullet.
In my experience, the .30-06 works wonders as a small game round when loaded with cast bullets. It works well as a varmint rifle when loaded with bullets under 150 grs. It works well against medium game when loaded with bullets from 150-180 grs. It works well against big game and dangerous game when loaded with bullets weights over 180 grs. The '06 performs well on the rifle range when loaded with the appropriate match bullet, and in my opinion gives up little to the .308 in terms of long range accuracy.