Own both and Love both.
If I had to make a choice for a SHTF rifle I will go with the AK.
#1 reason being that no matter what IT WILL GO OFF, just like my glocks. I think no matter how bad I treat it the thing will still shoot. There is a video someone posted of a guy shooting a full auto AK till it catches on fire. The guy keeps shooting the AK while its on fire! The thing never hiccuped through the entire ordeal! In the worst case scenario I may not have time to give my AR the TLC it needs to run flawlessly.
Reason #2 is the 7.62X39 round seems more devastating. Ive never shot anything but paper with either rifle but to me its like the 9mm VS .45 debate. The bigger bullet cant be a bad thing, and I would want deep wound penetration capable of smashing through bones and hitting vital areas. It seems like its easier to accomplish this with the 7.62X39 round. Ammo can still be found pretty cheap, and AKs are generally not picky about what you put in them.
Just so you dont think ARs suck, My Bushmaster AR has been flawless. It is my work rifle and I trust it to save my life while on patrol. As long as I take care of it, it will take care of me! It is extremely accurate, and has been VERY reliable. To date the only malfunctions Ive had were ones I induced.
Both rifles are highly modifiable. Both can accept scopes, tac rails, lights, and lasers. I think parts for AKs are going to be a tad bit cheaper. If your on a limited budget and want to be able to accessorize get an AK. The rifles are generaly cheaper and will leave you with cash in hand for extras be it ammo or accessories. There are many AK manufacturers so be sure to shop around.
www.atlanticfirearms.com has a very good selection to choose from.