I have to add my two ounces of lead to this discussion
First off the NATO round is 7.62 x 51 mm (.308), the 7.62 x 54 is Russian.
It was supposedly a downsize from larger .30 caliber rounds, but many of the old guards were unprepared to sacrifice range and hitting power, sufficient to create a lighter bullet suitable for a fully automatic assault rifle - though the HK G3 and Swiss SiG are notable exceptions. Since then, the switch to 5.56 was a far more drastic change, and in my opinion overdid it.
The supposed advantage of carrying twice as much 5.56 ammunition seems to be outweighed by the tendency to spray on full auto, instead of well placed shots. I know there are times when that is what is called for, especially when surprised at closer ranges, street fighting, ambushes etc. But overall, the tendency to adopt such small calibers seems like a poor substitute for good training and marksmanship if you have the time to develop it. Having a rifle light and fast shooting for the semi-trained masses, may not be the best choice for a smaller cadre of professional soldiers. As an historical example, the peacetime British Army before WWI had as basic rifle qualification, the ability to hit a target ten (or fifteen ?) times in a minute at 900 yards, with iron sights, and 10 rounds on target in 30 seconds at 600 yards. The Germans thought they were coming under long range MG fire when they first encountered the Lee Enfield at Mons. Not everyone aspires to that performance, but myself I would rather not be caught dead armed with a 5.56mm rifle in some tactical situations.
1. greater range - I would put my money on a good shooter with an FAL at >600 yards, over two guys armed with AR-15s.
2. windage - in a modest cross-wind, load up some tracer and see what happens to your 5.56mm bullets on full auto vs .308.
3. bush light cover - even at the shorter ranges, lighter faster bullets will be deflected by twigs, whereas the .308 can go through the bole of 4-6" diameter softwood trees.
4. hitting power - Supposedly the tendency of the .223 to tumble on impact equalizes this somewhat, but I would not count on wounding enemy soldiers to tie down adversaries in battle conditions. Numerous stories of assailants with six 5.56 wounds still standing. One hit from a .308 in the center of mass or even a limb, and that man is down. They don't even allow .22 caliber arms for hunting for that reason, its considered 'inhumane'.
5. Flak vests, light composite armors - substantially reduce the impacts from light bullets at ranges that would not stop a .308.
Complaints were also registered from the combat troops forced to used the M16, who averred that presuming they could get the rifle to work at all, two and three hits were required to drop one enemy soldier, whereas a single hit from a 7.62 NATO round dropped an enemy every time. The dispute continues today.
Regardless of the M14 having disadvantages in jungle warfare, 7.62×51mm NATO rifles stayed in military service around the world due to several factors. The 7.62×51mm NATO has proved much more effective than 5.56×45mm at long ranges, and has since found popularity as a sniping round.
In essence, there is still a place for both.
Now the AK-47 with 7.62 x 39 is something else, and comparing that to an AR-15 5.56mm isn't quite so favourable. The right compromise ? The Swedes had it close with the Ljungman 6.5mm semi-auto, also the Czech 7.62 x 45, or the 7mm British bullpup mentioned. A well designed modern rifle could handle something like a 6.5mm on full auto or burst with a reasonable amount of control, giving the most lethal combination for most situations.