i have both, ak in 7.62 and ar in 5.56.
AR thoughts
incredibly customizable - anything from a SHTF gun to varminting.
accuracy can range from very good to incredible depending on how your gun is set up and the ammo you use. My varmint ar can do 1/2 inch groups at 100 yards with black hills 52gr match ammo. Ammo choices are huge, from 40gr up to 77gr, and all styles of bullets.
very low recoil.
great ergonomics and fairly low weight. Ammo doesnt weigh a ton either.
AR's tend to be a bit pricey.
good quality mags can be had for $10 and are lightweight.
AR's do get tempermental in the following circumstances.
If they get excessively dirty (like not cleaning them after firing a 1000 rounds or after shooting dirty ammo like wolf) or over lubed. It's been my experience most AR owners (including myself at one point) over lube the guns and dont clean them properly. Clean them the right way, dont over lube, and they do fine. I had a rifle class where i shot 500 rounds of laquer coated barnaul without issues. AR's DONT need much lube to run.
If you need to count on an AR for SHTF, use GOOD quality mags and ammo (wolf is fine for the range, but not for bad guys) like Q3131 or blackhills. Stick to USGI type mags like D&H, Cproducts, etc. They're cheap and reliable.
AK thoughts
Probably the most reliable semi automatic rifle known to man. You can abuse the hell out of em, rarely clean em, shoot the crappiest ammo, etc, and it will still shoot.
AK's are fairly cheap, $300ish for a cheap one, better quality ones are $500-700
Recoil isnt bad, but it will get your attention.
Tend to be a bit heavy compared to AR's, and the mags and ammo arent light either.
Not much in the way of ammo choices. Fortunately the mags arent expensive, a little hunting will turn up piles of $10 commie mags that are indestructible.
Ergonomics are so so, not great but not horrible.
Accuracy is fine for minute of bad guy, but you wont be varminting with an AK. Effective range (due to accuracy) isnt as good as an AR.
one nice thing about AK, for self defensive uses, pretty much any kind of ammo it chucks will work great (even wolf), as opposed to an AR where you want to use the right kind of ammo for the job at hand.
Not quite as customizable as AR's (AK's arent suitable for a lot of things that AR's are good for)
AK ammo tends to be cheaper then AR ammo.
Cleaning an AK is a snap. And its a lot more tolerant of cleaning styles: if you over lube, or dont do a very good job, the rifle will still fire reliably.
Summary thoughts
AK's are fun guns for plinking, and a good choice for defensive /shtf situations. If thats all you need from a rifle, then definitely consider an AK.
If you want better accuracy, more flexibility, less weight,and are willing to learn how an AR works and how to take care of it (its not hard, just takes a little learning), then the AR will work for you.
Of course, you can do what I did and buy both