BigMike, The AK is more powerful, ammo is easier to come by and cheaper, I think it's a bit stronger when it's getting beaten up, and should the SHTF, ARs and the ammo will be plentiful, either from trading, military, other civilians, or dead bodies.
Something to consider - the AR was adopted by the military for several reasons, which may or may not correspond to your wants and needs. The U.S. Military wanted to replace the M1 because of complaints by troops. They wanted a weapon that was:
Had less recoil,
was a smaller caliber so the troops could carry a higher number of rounds,
Had a larger capacity box magazine,
was smaller to accommodate a wider size range of soldiers.
Another reason for changing to the 5.56mm round was attrition. If an enemy soldier were killed, only a single soldier was removed from battle - a job the 7.62mm did well. However, if that same soldier were wounded, two other soldiers had to stop what they were doing and remove him to the rear echelon to be treated. It would take time for them to rest, re-equip, re-arm and get back to the line. So one wound = three soldiers removed from combat, at least temporarily.
Now, the AK is a lighter recoil than the 7.62X51 NATO, being only 7.62X39, which also means the weight falls right in the middle between that and the 5.56mm. It already has the larger box magazine at a standard 25 rounds to the ARs 30. The AK is very easy to carry and has many configurations, so the only question becomes if you are comfortable with the manual of arms. If you are not an exceptionally light or small-framed person, then it should be workable.
So if your objective is to terminate with extreme prejudice instead of wounding people so they can be removed for treatment, then the AK is the way to go with its larger bullet, similar recoil, capacity and weight. Lots of accessories (cheap, too!) from hundreds of sources that are new manufacturer to ex-Russian military.
I hope it helps!