Short or long (actions, that is!)
Since the opinions seem to confirm little preference in action length, that sure shoots the reason for getting a 308, instead of a 30-06!
A 30-06 is much better for reloading, including a great variety in bullet weights. Also, a much better variety of powder that can be used efficiently in the 30-06. Shortly after the 308 came out, many of the multitude of professional gun writers around at that time, stated it was quite difficult for the handloader to equal factory loaded velocity in the 308. They said powders had to be developed especially for the 308, in order to achieve the factory velocities. With the pressure limits lower for the 30-06 than it is for the 308, or 270, it is easier for an experienced reloader with a modern bolt action rifle, to attain considerable more power, especially with heavier bullets, than is possible with the 308.
Lighter recoil with the 308, you say? Then load the 30-06 a bit lighter. It is very adaptable for lighter, accurate loads.