AK vs AR

Here is my take on AK (Kalashnikov) style rifles vs AR-15 style rifles.  For simplicity's sake, I will consider AKs in 7.62x39 and ARs in 5.56x45 NATO. I own both, and I like both, and I have experience running both in carbine classes, for whatever that's worth.  AKs and ARs have different design decisions.  In general, the design decisions that give one its strength, also give it its weaknesses.
That said, ARs are more reliable than people think and AKs are more accurate than people think, and it's really just a matter of preference.

AR advantages:
- Lighter, in part due to having an aluminum receiver and no piston and a lighter, hollow bolt carrier.
- Lighter and smaller magazines and ammo.  Since the magazines are more or less rectangular, they are easier to stack and fit into boxes or dump pouches compared to the curved AK mags.
- More accurate, in part due to tighter tolerances and lack of a heavy bolt carrier and piston slamming around.
- More ergonomic controls, especially the safety which can be manipulated very quickly with the thumb, and the charging handle which can be run with the left hand easily.  The AK has the charging handle on the right side of the gun, which makes it a little awkward to run with the left hand, and it has the safety forward on the right side of the gun, which requires breaking the firing grip at least somewhat to manipulate it.
- The bolt locks back when the mag is empty, which lets you know when you're empty and enhances the speed of emergency reloads.  AKs do not have this feature, and with an AK you usually know you're empty when you hear the click of dropping the hammer on an empty chamber.
- The bolt can be locked back manually.  There's no way to lock back the bolt period on a stock AK, although aftermarket selectors with a cut out to allow locking the bolt back are available.
- The sight radius for iron sights is much longer, since the rear sight is at the rear of the receiver. On an AK, the rear sight is relatively far forward in the middle of the receiver, leading to a shorter sight radius. Also, an AR's aperture style rear sight is generally considered more accurate than the AK's notch and post sights.
- The process of reloading the AR is a little bit faster than that for reloading an AK.

AK advantages:
 - More intrinsically reliable and low maintenance. Here are some factors that play into the AK's reliability:
    - The bolt carrier and piston are heavy, and the system is 'overgassed', i.e. the amount of gas that is transmitted through the gas tube to the piston is significantly more than is strictly needed to cycle the bolt.  These factors help the bolt smash through friction due to dirt or lack of lubrication, but also hinder accuracy.
    - The stroke of the bolt is significantly longer than what would be needed to extract and eject the empty case and feed a new round from the magazine.  So weak or erratic ammo is tolerated.
    - The 7.62x39 and 5.45x39 cartridges are both tapered more than 5.56, so extraction is enhanced.
    - There is a lot of room in the receiver.  Dirt, blown primers, or cases that fail to eject have enough room to generally not get stuck and cause problems.  Compare to the AR, where there is exactly enough space above the bolt for an empty case to get stuck, and exactly the amount of space in the gas key for a small rifle primer to get stuck.
    - The extractor on an AK is large and beefy compared to that on an AR.  The ejector on an AK is a fixed piece of metal integral to the receiver which is simple and robust.  The ejector on an AR is an assembly of little parts in the bolt which includes a pin, the ejector, and a spring.

- The recoil spring is in the receiver, unlike the AR which has the recoil spring in the stock.  So AKs can have folding stocks.
- An AR's bolt carrier has holes in it that can allow dirt and grit to get inside the bolt carrier if the dust cover is not closed. An AK has a solid bolt carrier with no dust cover needed.
- Some malfunctions on an AK are generally easier to clear.  In a double feed, the magazine can be removed without needing to lock the bolt back, so the procedure to clear it is to simply remove the magazine, rack the bolt a few times, and reload. Clearing a 'brass over bolt' malfunction in an AK is made much easier by just removing the top cover and then picking out the piece of brass.
- The rock and lock magazine mechanism on an AK allows easily seating a full magazine when the bolt is forward.  On an AR, many users load their mags to 28 or 29 rounds to ease seating the mag when the bolt is forward.
- Ammo is generally cheaper for the AK, especially if you can find military surplus ammo.  AKs run well with cheap steel cased ammo, which can be hit or miss in an AR.
- An AK is less expensive than a comparable AR.