Generally the issue is actually shooting .308 out of a 7.62, as the cross compatibility issues are not the same as the .223 and 5.56. With the .308, the use of slightly slower burning powders and heavier bullets (this optimizes muzzle energy in bolt action firearms which generally have longer barrels than military arms) can cause damage to some 7.62 NATO firearms' gas systems (the M14 is a prime example), in addition, from what I understand, the 7.62 NATO has a thicker webb than a .308 to prevent case head separations in machine guns. The maximum pressure for both is more or less the same (SAAMI Max pressure is slightly higher than the NATO EVPAT listed pressure, CIP lists it as the same pressure as NATO).