It's a number of factors.
I'll not discount that ammunition quality, iron sights, and recoil MAY have some impact, but I do not believe that those are the primary issues.
I believe tolerances and mechanical operation are the issues.
I base this purely on my own experieces shooting:
-Centrury SAR-1 7.62x39 (AK-Pattern)
-Vector Polish underfolding 7.62x39 (AK-Pattern)
-Saiga .308 converted w/ 8X PSOP optic (AK-Pattern)
-DTI kit build M4-gery 5.56mm (AR-15 Pattern)
-DPMS LR-308 24" Stainless Steel heavy barrel w/ Leupold 3.5-10x40 Mark 4 optic (AR-Pattern)
My Century SAR-1 using iron sights shot 5"-6" groups at 100 yards. It was put together by a manic-depressive, alcholic monkey that had been subjected to a lifetime of shock treatments.
I wouldn't take a shot that mattered at anything I needed to take an ethical shot at. Ever.
Conversely, The Vector polish underfolder shot pretty damned good with iron sights. I never measured its groups, but I'd wager that it could do 2"-3" groups based upon the size of the things that I shot with it. I really never missed what I was aiming at. I realize that isn't all that "scientific," but I am not a range shooter. I shoot on my private land.
So at this point, we have two AK pattern rifles that are both using iron sights. One is a 5"-6" shooter and the other is a 2"-3" shooter. Obviously, it wasn't the iron sights that did that.
It wasnt' the ammuniton, either. Both were shooting Wolf Jacketed Hollow Points from the same lot.
Shouldn't have been the recoil. Both were 7.62x39. Hell, the better shooting one was using a flimsy and less comfortable underfolding stock. The Century had a Warsaw-Length wood stock with a 1" recoil pad to increase the LOP.
Now let's look at a couple of other things-- first caliber.
I had a Saiga .308 conversion that I was trying to make an accurate deer rifle out of. I replace quite a bit of parts: Stock, grip, and trigger. I shot only high quality factory loads in the rifle. And I had optics mounted on the rifle.
This rifle was chambered in .308 Winchester, not 7.62x39. It also had optics in place so the iron sights were not a factor in this consideration.
I pleased on the on-set with its accuracy, but it was nowhere consistent enough for me to put absolute faith in it. My best group was 1" at 100 yards. My groups were more often 1.5" at 100 yards. Bear in mind that this was benched shooting with a LOT of careful time taken in the shots.
What concerned me about the rifle is that the shots became erratic as soon as the barrel started heating up. Groups would disintegrate after about 5 shots.
Saigas are known to be probably the most accurate rifles in the AK line, and from what I've seen, they are. Bear in mind-- when I say that my groups disintegrated after about 5 shots, I am really talking in terms of a target rifle. The "disintegration" amounted to about 3"-4"-- which was still great for what it was, but NOT great for an accuracy-built platform that I had sunk $950 into.
Conversely, I sold the rifle to fund another project built with the same goal in mind: An accurate semi-automatic "precision" rifle.
I bought a DPMS LR-308. I am still working on this rifle-- it needs a new trigger in the worst way.
However, using a Leupold Mark 4 3.5-10x40mm illuminated Tactical Milling Recticle optic and standard rings mounted directly to the receiver above the bore, and using quality factory ammunition-- Winchester Ballistic tip 150 grain cartridges-- the best group that I have achieved with this rifle at 100 yards was 0.38 inches.
Now, I haven't shot this rifle enough to know what my typical group is. However, I have NEVER had a semi-auto pull of a 0.38 inch group. I would not expect this rifle to do that on a regular basis-- and I DO consider that a "cherry-picked" group. I can say, however, that I've not had a SINGLE group at 100 yards from this rifle that was OVER 1.00 inches.
Because I had to fight my crappy trigger, I anticipate that my consistency will only get better with a better trigger.
So, now we have two rifles-- both chambered in .308 Winchester, both using optics. One was a 1.5 MOA shooter at 100 yards for a FEW shots, and then a 3"-4" shooter at that range. The other was a sub-MOA shooter out of the box, and has pulled off a Sub-1/2 MOA group, and has never shown any group deterioration after shots. The former on an AK pattern, and the other on an AR pattern.
You'll notice that I left out of this discussion the most DIRECT comparison: My AR-15 M4-gery.
I have done this because frankly I don't shoot it near as often as I do the LR-308 at this time of the year. Its deer season, so I tend to focus on the larger calibers in the winter. I'll play with the AR-15 more this Spring and Summer.
However...
Like the Vector, my AR-15 has hit whatever I shoot with it. When I sighted the AR-15 in, I was able to produce groups that were under 1 MOA at 100 yards. However, I didn't sit at shoot it beyond the final "sight-in" group. I have no idea about what the rifle will do as it warms up-- although it DID get warm as I was sighting it and it seemed that there was no discernable effect on my shooting. BTW.. this rifle is using a chrome-lined 1:7 twist 16" barrel with M4 ramps-- nothing special.
Recoil IS non-existent with the AR-15 in 5.56. However, I can not conclude that this has impact on accuracy since the two .308 Winchester rifles both have more recoil, and both were more accurate than either of the AK pattern rifles that I compare them to.
I can't say that irons themselves contribute to accuracy issues as a primary cause. I saw two that were dramatically different in accuracy that both used the same iron sights. Plus, I had one AK pattern rifle (the Saiga .308) that was using optics. ALL of the AKs were significantly less accurate and/or less consistent than ANY of the AR patterns that I compare to.
Triggers seem to be an issue.
My Century AK had a Century trigger. It was FULL of slop and I hated it. Both the Vector AK and the Saiga .308 was using a Tapco G2 Trigger group. These two rifles had a MUCH better trigger break. I feel that this had a lot to do with why the Saiga and the Vector was more accurate than the Century.
However, it should be pointed out that both of my AR-pattern rifles are still using stock triggers now-- DPMS triggers. I don't care for either. Both are hard on the pull, and have more play in them than I'd like. Neither break as cleanly as I'd like. Both WILL be replaced.
But that said...
BOTH of the AR pattern rifles demonstrate significantly better accuracy than any of the AK pattern rifles that I've owned.
I DO think that the operating system has to do with something, but I can't quantify it. I've read the "experts" that say that the long-stroke piston gas system should have no impact on accuracy since the bullet should have left the rifle before the bolt cycles. Makes sense. But I think they are missing something. I DO think that this comes into play somehow-- I just don't know how. I do know that it seems that every long-stroke piston rifle that I've shot was less accurate than the direct-impingement rifles that I shot.
The final consideration that I have-- like others-- is tolerances. I DO think that this is perhaps the most relevent aspect. Someone once told me-- "You can have extreme reliability, or you can have extreme accuracy, but you can't have both."
The guy that told me that built 1911 "race-guns" that were incredibly accurate, but were picky.
The logic there is that tighter tolerances mean that they rifle will line up the right way, and there will be less variances between each shot. However, this means that there will be less forgivness from dirt, fouling, etc.
The reliable rifle will have more "slop" in every aspect. It will forgive more dirt, etc., and will feed and fire better due to having a looser chamber. That looseness also introduces more variance in the "line up" of everything that shoots, or how it shoots. That translates into less accuracy.
Based upon my personal experiences with both platforms, I think that there is a LOT to this line of reasoning. Science, be damned. I only know what I see.
I hope this long-wind post contributes something to this discussion.
-- John