I see the 762GM vs. the 308 GM as follows:
The 762 has ‘milspec’ features like staked primers and unpolished brass, for folks who look for them when using semi-auto platforms. Heaps more of those fielded sold recently, in commercial/LE/mil (LMT, LaRue, Sage, Colt’s new gun(s), etc.)
Federal’s ‘Tactical’ LE line has these features in .223 and 5.56x45mm. I don’t have the spec sheets in front of me, but I wouldn’t be surprised to see the ‘762’ as a higher pressure/higher velocity load than the ‘308’. The ATK 5.56 vs .223 split is spec’d at around +/-50fps.
I haven’t shot at 1kM in years, and that was with a boltgun. I do know of one band of merry men who took a gob of COTS Hornady 178gr Superformance .308 with them for hopeful usage at longer ranges. Best of luck to them!