I think you'd be surprised at how much carbon buildup affects the accuracy of a weapon. One of the biggest reasons people handload is because they get to experiment with different products and how much carbon they leave in the upper receiver / chamber.
I know there's a lot of variability between weapons, but that's simply not true. Unless you're talking about using some pristine match grade AK (if there is such a thing) versus an old M16 A1 or something, the AR-15 is just a far more accurate rifle by design. In fact, that's one of the only reasons the AR-15 is better than the AK. The AK-47 was based off of the SKS, which uses an very style old school gas piston. This is less accurate than (many) AR-15s gas impingement systems. Granted, although many ARs do use gas pistons, they're a different design than an AK's - which is literally just a piece of tube on the outside of the weapon. The reason is because the impingement system has less moving parts over the barrel than the gas piston, resulting in better accuracy. The AK's barrel also heats up quicker, (usually) has a shorter barrel, and is more prone to barrel wobble (as opposed to modern AR-15s free floating barrel systems).
Attachment 11044
This is the gas impingement system on an AR-15.
If you ask me, the biggest factor in the total accuracy is the shooter!
And as far as your claim about the M14 being more accurate at 500 yards, I'm going to have to call you out there. One of the biggest reasons the m14 was phased out was because the wooden furniture on it would swell in the damp jungles of Vietnam, resulting in horrible accuracy. The M16A1 wasn't exactly a tac driver, but the fact that it was made out of polymer and steel left it basically immune to swelling. Granted, they made polymer housing for M-14s, but that was way later.
Also, part of the reason the range is different is because we're talking about what's called "maximum effective range." A 7.62x54 is simply more effective at a higher range because it's a heavier round. You can still accurately shoot an AR-15 through paper targets beyond 300 meters, you just can't reliably kill a person with them.
There's also a difference between point target and area target, but I digress.
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