The SAAMI considers the 308 Winchester and 7.62x51 NATO to be interchangeable. Pressures are actually slightly less with the NATO round. The only problem sometimes encountered is that certian military rifles (the m-14 / m1a1 being prime examples) are designed to operate within a certian bullet weight (147 grain), and powder burn rate, and can suffer damage to the rifles operating rod if commercial ammo with the wrong burn rate is used. Also, some military rifles, due to firing pin design, are at risk of slam fires with commercial ammo using soft primers. Max pressure in the 308 is 62,000 psi, with the NATO round being 60,000 and some change psi.
I have used various military surplus NATO ammo in my bolt action commercial guns for years without issue as cheap practice ammo, the only problem being that I have found some brands have primers a little to hard for reliable ignition in my Kimber .308
Larry