The only 308 Win rifles that I am aware the CMP sells are not Navy rifles, but rifles that the CMP puts together with military parts and new Criterion barrels. They call them "Special Grade". They run about $1000. They do sell some Navy barreled actions, but they are just barreled actions and run $350.
The 308 rifles are just as reliable as the 3006 rifles. All other things equal, there is no advantage in mechanical accuracy between the 3006 and the 308. However, in practical terms, the 308 causes less fatigue, and over a course of fire, the typical shooter will perform better with the 308 due to less fatigue.
As to ammo availability, I think it is probably a wash. However, the full length Garand is pressure sensitive, and you can bend the op rod with the wrong ammo, unless you use a gas regulation device like the Schuster Plug. An alternative is to send your Garand to Shuff's for a Mini G conversion. The conversion shortens the op rod and reduces the opportunity for damage do to improper pressure curve.