BigBlueBox. Is it too late to rename this thread as WI: the USA chose something other than 7.62x51mm? The posters have pretty well ignored NATO.
Part of the problem with the OP is that he is mandating the British .280 round, which was intended to replace all other rounds, while at the same time saying they'd maintaining a heavier round for sniper and and MG roles. If you're going to have a two caliber standard then the .280 is pointless, as it was meant to replace the .303 entirely in all roles. They'd have been better adopting a 6.5mm as rifle/lmg round and maintaining the existing .303/.30-06 standard for MMGs/sniper rifles, but instead tried to keep the one round standard and created a flawed compromise round that wasn't good enough in any role to justify it.
Certainly the .270 was a better option then the .280 if they were going to try to make a modern assault rifle, but then would have to keep a 7.62 full powered round as OP suggests, though IMHO even the .270 is overpowered/overweight for a rifle round given the knowledge gained in WW2 about engagement ranges and recoil impact on automatic fire.
Nevertheless assuming that became the NATO standard, that is the .270 with a standardized 7.62 full powered round with M1 style bullet (say something more powerful than the 7.62x51 NATO of OTL), that would have been quite a bit better than what existed IOTL. Question is whether it would be in service in time for Korea given the post-WW2 budget cuts and huge stockpiles of left over equipment that the US relied on for years after WW2. Assuming the Brits still go their way and the Canadians follow, they could well have the EM-2 in .270 for Korea (with all it's potential flaws) and beyond. Not sure if that makes any sort of difference considering their limited commitment to Korea.
In Vietnam though that might make a bigger difference if the M-14 or whatever US weapon is selected is in .270 and works well with it, especially if there is some sort of SAW variant in that caliber. It would be highly interesting if the AR-10 was in .270 and beats out or replaces the M-14. If there wasn't the burst barrel in the torture test, which might not happen given the lower pressures of the .270 round, perhaps the AR-10 might have been given a go instead of the M-14.
I cannot see the FN FAL getting adopted by the US in any circumstances given the attitudes of the day, even if or perhaps especially if the British .270 is adopted. The Brits too would probably keep their EM-2 unless it fails in the field. So the FN FAL might remain a rather small production weapon ITTL, especially if the AR-10 is a competitor.
Vietnam with the US squad standardized on the AR-10 in .270 would be pretty interesting and would have given the AKM a run for it's money.