7.62x51mm NATO IS of lower pressure than 308 Winchester. 223 Rem vs 5.56x45mm NATO is where the reverse is true, the military round is hotter.
Which military guns can take full power 308 Winchester is a tough question to answer. In some cases it's an educated guess, but there are real answers. Thicker brass in military ammo means more friction on chamber walls without brass stretching, meaning less rearward thrust on the bolt.
G3s should only be used with NATO ammo, although they are marked 308 by US assemblers. Their recoil operated action would be sensitive to these pressures though and the reduced frictional resistance is a big deal. I previously used 308 ammo in my G3 and the recoil was immensely higher - that would be the bolt slamming way too hard.
FALs were only designed for NATO ammo, but the availability of US made ones with no warnings suggests that using 308 ammo is ok, but adjusting the gas system is a must.
The M1As are advertised by a US company as being able to take 308 Winchester ammo, so I doubt there's any problem. Wear may be a different story.
The Saiga-308s have a distinctly different three lug bolt from the two lug bolts of other 7.62 NATO AKs. I believe they were designed for 308 Winchester if they were aimed at the US sporting market. AK margins most likely allow equally good operation using 308 or 7.62 Nato ammo.
Here's where there may be a problem - The small ring Mausers were designed for much lower pressures than the large ring Mausers. Some of these were converted to 7.62 NATO after it was standardized. These include the La Guardia Mauser and the FR7. There are others I don't know of, but 7.62 NATO small ring Mausers aren't the safest bet with 7.62 NATO ammo. The FR-8, however, is built on the 98 Mauser action which is certainly strong enough for full power standard rim rounds, of which 308 Winchester is one.
In short, anything chambered for 308 Winchester can safely take 7.62x51mm NATO, but not always the other way around (usually though). Anything chambered for 5.56x45mm NATO can use 223 Remington ammunition, but not the other way around. This is actually an issue more often as 5.56 rounds may not chamber in a 223 barrel.