Breaking it down:
First of all, caliber counts, What you are going to shoot determines what cartridge determines what kind of rifle. With "plinking" it's a toss up. With "self defense" both are capable. Costs of ammo, about the same, they compete for cheapest on the earth because both are government subsidized.
With AK ammo you have to watch for any future bans. With AR ammo you have to watch for any future bans. Kind of a draw.
Ballistics, the 5.56 has longer, flatter range and is more lethal. Really. Sorry AK fans but the low powered import junk that powers them isn't up the level of XM reject government wholesale products dumped on the market by the contractor. AR ammo at the lowest cost is better. Move up to $1 a round commercial hunting or precision loads and sorry, the AR is still flatter, more accurate because of that, and can deliver lethal amounts of power to it's outer range. It can do that because AK ammo has more bullet drop which causes it to be less capable and have less range.
Just because it's .30 doesn't make it better. Sorry. It's why we weren't pinned down in Afghanistan with AK's - the insurgents didn't even try, they moved way up to Russian .50 cal to have a decided 1,000 yard advantage.
If you could find a Finnish Valmet in 5.56 and shoot it side by side against an AR , then the gun itself becomes an issue. The AK does not help the shooter - if anything, it defies you to being capable within a few hundred rounds. The AR was designed to become easy and familiar very quickly. First, the magazine catch can be operated by the trigger finger when it won't be doing something else, and does NOT require you to remove your hand from the grip. Second, the bolt hold open - the AR holds the bolt back on the last shot. Push button, drop mag, insert other with off hand, hit bolt catch with off hand, BCG chambers round, and you don't even drop your eyes from the sights.
AK? Sorry. You have to drop the mag with the paddle catch off hand, then insert the magazine AGAINST THE CLOSED BOLT, which adds the spring pressure of forcing a fully loaded magazine up against it. Then the bolt handle has to be grabbed by the trigger hand to cycle it to chamber a round, which loses seconds getting it back in action. Your hand is off the grip and your eyes are often off the sights.
AR's are easy to keep in action firing rounds, AK's defy you to be either good or fast. But if it's a plinking rifle that is moot. Combat speed isn't critical.
Self defense? Not. It's critical, and it's one reason why you see very few AK's in the upper ranks of 3Gun competition. It's usually as a statement of principle than one of being better.
Accessories? AR hands down. Far more of them, and when you look at AK accessories none are coming in from overseas. They are all derivatives of AR gear adapted to the AK with workaround mounts.
Brings us to optics - the AR has a picatinny quick mount rail on the top of the upper receiver, the AK has a bolt cover that isn't suitable for much else as it's not secure and wobbles. AK optics are about as easy to mount as red dots on lever actions. You can use the same ones, but the mounting plates and adapters are low production higher cost units.
Maintenance? They are both self loading actions, which means they both dump gas residue from the barrel past the brass as it opens the action. Both do it, just like the HK or FNFAL or ARX or any other blowback, including all the auto loading pistols. The action will get dirty regardless. With the AR you shotgun the upper, pull the BCG, tear it down, and when you extract the bolt you are cleaning the gas pistol and cylinder.
Do that to the AK and once the bolt is out, you still have to pull the upper handguard off to get to the gas cylinder. AK maintenance is actually more complicated and requires more work. Not much more, but it's more none the less.
However, most fans won't accept these facts and complain it's trash talking. Sorry, facts are facts, and it's why even the Russian Staff is trying to get away from the AK altogether. Budget and tradition make it hard, but they are in print saying they would like a "modern" firearm. China DID, the AK is built for export, not for use by their armed forces. They moved to a locally designed bullpup. But that's fodder for another thread.
When people ask "Which is better?" there is always an unspoken element of "Which gun does everyone think is superior, which will reflect on me as being the better smarter guy?" Well, depends. Some don't actually want the better technologically superior piece, they give bonus points to tradition, or thumbing their collective noses at certain groups associated with a guns use. In that, nobody can give which is better.
Focusing on the gun along, it's the AR hands down- which is why more nations are adopting them while those with AK's are looking around to give them away. Only in America do free citizens see the AK as something good - everywhere else in the world, not so much. It's either the symbol of an existing oppressive government, or a symbol of the one that's to come. At least the AR already established itself as the symbol of America, for what it's worth. And it seems from the number of people trying to get here that it's not so bad after all.
Hey, they could own one themselves. Or an AK. It's a free country. Buy what you want, your reasons are good enough for you.
For further commentary reaching back before the internet was started up:
http://www.bing.com/search?PC=WCUG&FORM=WCUGDF&q=AR+vs+AK&conversationid=