I was pretty sure I'd read differently, and a quick Googling turned up this page: http://www.303british.com/id36.html
From what it's saying, the 7.62x51mm brass is thicker than .308, the chamber is typically a bit larger, and the .308 is actually loaded to slightly higher pressures:
'Commercial ammunition has a SAAMI/ANSI maximum pressure of 62,000PSI. '
'Military ammunition is loaded to maximum average pressure 50,000 CUP (approximately 58,000 PSI using the modern piezo transducer method of measurement). '
I know that's not the only place I've seen it, but I'm certainly no expert.