I probably know more about this topic than most, as I use an AK in 3gun, and do pretty decent. Really good at the state level, but not a lot of national matches under my belt.
Now first off there is a reason that the AR dominates 3gun. It is easier to shoot faster, with a greater degree of accuracy, and it is easier to reload, primarily because of the bolt hold open.
Hard core 3gun is not real friendly to cheap AKs. Just like it isn't friendly to cheap ARs. It is pretty intensive as far as the shooting games go, and requires a good rifle to be competitive. Don't get me wrong, when you are starting out, bring whatever you have, and have fun.
But if you want to do good, you are going to need the more accuracy the better. I don't use a cheap parts AK. I use a Vepr, which is a sub 2MOA gun. I've also replaced the buckhorn sights with Krebs dustcover peep sights. The more accuracy you can squeeze out of your gun the better.
Mag changes can be just as fast, but it take A LOT more practice. And that is only if you plan ahead and never shoot it dry. If you have to work the bolt, your reload will be a ton slower. The rock and lock can be done very quickly, but you need to practice more to be consistent and fast with it.
The safety is harder to use, unless you have mutant gorilla length fingers, then it is actually faster. (I index my trigger finger on the safety, at the buzzer that thing comes off as my finger moves to the trigger).
So an AK can compete (at least at the state level) but you need a really good AK, and you need to practice the heck out of it. For most shooters they are going to go farther with an AR variant. We had a rifle only match a few months ago. All 3gun style shooting, but all rifle. Ranges from CQB to 200 yards. I took 2nd overall, and 1st iron sights, and this was in a field of 50 shooters, many of whom are very very good. But as was pointed out by the 1st place gun (
who beat me like a red headed step child) if the ranges had been increased then I would have lost to more optics shooters, and if there had been more mag changes I probably would have lagged a bit more also.
For the 400 yard shots, that is why I just bought a .223 Vepr.
Keep in mind that your scope mounting options with an AK are more limited than a flat top AR if you decide to eventually run optics.