Yeah, no, they don't. If that were the case, you'd see people using AKs to win rifle competitions.
In my experience, an off the rack Arsenal AK74 with military surplus ammo will hold its own against an off the rack Colt 6920 with military surplus ammo. There is certainly much more one can do to improve the AR's accuracy which would certainly give it an advantage in many types of competition.
I'm a bit surprised you don't get better accuracy out of your Colt, though. In most cases, even bone-stock M4-style rifles with surplus ammo should shoot around 2MOA.
2 MOA is very doable with Saigas in my experience. When people start talking about accuracy with ARs they seem to be referring to that of high end guns with high quality ammo and fail to account for the fact that ARs run the gambit as does the ammo that may be shot out of them. A saiga will not keep up with my Noveske or other free floated ARs with high end barrels. Of course, neither will a lot of other ARs. ARs do tend to have sights that are more conducive to accurate shooting than the AK open sights. My experience is that using a 4 MOA aimpoint and shooting from field positions with wolf ammo accuracy isn't noticeably different between my Novekse and my .223 saiga. They same is true when shooting other makes of AR with surplus brass ammo. If I want to change things and shoot for absolute accuracy the Noveske can surely blow it out of the water.
The AR is the better gun for 3 gun and the like and I think much of it is for reasons apart form accuracy.
I may have missed it but what is the OP's purpose for this gun and what type of AR is he looking at. I have said for a while now my preference in guns is:
1. Nice AR
2. Nice AK (saigas, veprs, etc)
3. other AKs
4. Other ARs
If the gun is a range blaster then a decent AR or a decent AK with both be fun and the cheaper ammo of the '74 could swing things. If it is a competition gun then a good AR is hands down the winner. If it is a self defense gun then either could work but my preference is the order listed above. Before I could every say AK or AR I need to know what AR we are talking about and the intended uses.
One thing to consider is a lot of money can be spent on an AK, that was originally bought to save money, trying to give it the feature of an AR. In fact the cost can quickly exceed the price of a very serviceable AR.
This is exemplified by something I find curious, the fact that the Suarez people after years of deriding the AR and trumpeting the AK, and bemoaning any one for "trying to turn an AK into an AR" have finally taken to doing just that. If you look at what they are doing these days they are basically trying to make an AK have the features of an AR. They have gone to using 5.45 guns. They are trumpeting the TWS rail and either ultimak gas tubes or now the TWS hand guard with top rail. Basically this is an expensive way to try and get a flat top and a quad rail. They are putting magpul stocks on them and replacing the commie muzzle devices with US flash hiders. There is a lot of discussion as of late about how to add folding BUIS.
Lets run the prices:
Saiga in 5.45: approx $330
Basic conversion w/ parts Suarez trumpets: $200
TWS dust cover: $150
TWS hand guards and top rail: $270
Thread barrel: $50-100
Flash hider: (we will say a cheap A2) $10 (but could be $80 for a vortex or the like).
Stock adapter: $90
CTR stock: $90
Basically you are now looking at a $1200 AK that still falls short of a similarly priced AR in a number of respects.
I'm not against updating AKs but I think from an economic standpoint if one wants the features of an AR they should get an AR.