Apparently, and I am not at all sure of the actual metrics, but I have been recently instructed that the two rounds are not quite identical, and one should not use the MILSPEC ammo in a civilian .308. Or is it vice-versa?
I date back to the M-14, and also have hunted with a .308. The .308 is a great round, and easily available in all kinds of interesting loads.
I think it's you should not use civilian ammo in a military-type rifle without checking its suitability. I managed to damage my Garand by using 30-06 ammo that was intended for bolt-action rifles, and was WAY hotter than WW2 rifle specs.