The SSAMI recommended pressures for the .308 Winchester and the .30-06 Springfield are 62,000 PSI and 60,000 PSI (50,000 CUP) respectively.
If I can quote the Sierra manual previously referenced "Shortly after the end of World War I, the U.S. Ordnance Corps began looking for a smaller cartridge to replace the 30-06 Springfield." If I may continue, "By 1944, engineers at Frankford Arsenal had begun to experiment with the 300 Savage case. Designated as the Cartridge, Ball, Cal. 30 T65, the experimental round gave performance roughly equal to the larger 30-06. After a long series of modifications, a revised cartridge case designated as the T65E3 was adopted as the NATO standard on December 15, 1963. The U.S. finally embraced the 7.62mm NATO cartridge in two new weapons adopted in 1957 - the M14 rifle and the M60 machinegun."
I will say that the 7.62 x 51, when adopted was produced at a lower CUP than the pressure of the current day .308 Winchester and it is not recommended that one shoot .308 Winchester ammo in a chamber labeled 7.62 NATO. Not necessarily because of the pressure, but more the issue of headspace. I will also say that because of the larger capacity of the .30-06 case and the availability of the slower burning powders you can increase the velocity and energy of that great old cartridge. But that was not the point of the original post.
'nuf, 'nuf.