I'd take the AK, even though I own AR's that have been perfectly reliable for hundreds of rounds even uncleaned.
"Battle" I assume is war. War is dirty. Rather have an AK. I'm assuming I have full auto choices in each? In battle, spray wins and there's little care for collateral damage. All the combat video I've seen (AK or AR) shows people hammering away full auto at the approximate position of the enemy. It is rare to see well-aimed fire at specific targets.
Battles and wars can drag out for days. Not a lot of time or energy to clean. In a battle, it is safe to assume it will be outdoors, possibly in sandy, muddy, or frozen regions. There's a good chance you'd have to crawl through whatever is on the ground...
For SHTF/Defense, I prefer the AR. Say there is mass looting or rioting, I need speed and accuracy. Being home, there's no full auto option - so in semi the AR I think is better. At home, I can keep the rifle spotless clean and well maintained. Even if I had to bug out, there's really no situation in the South East, even under SHTF conditions, that would render the AR useless due to environmental conditions. If anything, it is well suited for the wet humid climate. Also, in a domestic situation, I have the time (most likely) to arm myself with a sidearm. That's a good idea no matter what rifle you have.
Reliability when extremely filthy is an advantage of the AK that isn't really a practical advantage for 99% of the people living in the United States. Having a rifle that can survive being buried in sand or mud isn't that useful due to the fact that a situation like that is far less likely than the already extremely rare situation of even having to ever use a rifle like that in a SHTF.
There's just not enough filth in a domestic situation to make that aspect of the AK a serious factor. If you have your AK at home, sitting in the safe or closet, then there is no reason why you shouldn't field strip it, totally clean it spotless, and oil it well. When or IF that rifle ever needs to go into action, it will do so clean, just like an AR. Say you have a battle pack, and your load out is 180-210 rounds. Both the AR and AK can shoot through all of that without a single stoppage. 2,000rd uncleaned "torture tests" really prove nothing, unless you plan on being in a SHTF where you can't clean your rifle for 2,000 fired rounds. I doubt you'd carry that much, and if you were shooting it out from home and needed that many rounds, it means you were up against the military or an entire LE dept - in which case you'll be dead.