OK, think of it this way. The capacity of a battery is a measure of how much total energy it can store and deliver into a load. In this case lets say both are rated at 2000 MAh. If these batteries had a "C" rating like Lixx batteries do, this would give us an indication of the rate these batteries can deliver that power into a load. They don't so I will make up some values here for illustration purposes. The smaller AA cells may only be able to deliver their energy into something like a 200MA load over a 10 hour period and still be able to deliver their full capacity. The larger sub "C" cells may be able to deliver their same amount of stored energy into something like a 1 A. load for two hours. Note that 200 MA spread over 10 hours equals the 2000 MAh capacity. Likewise, 1A. spread over 2 hours equals the same 2000 MAh capacity. In other words, the larger batteries can deliver their energy at a much higher rate than the smaller ones. Keep in mind these values are arbitrary just to make a point. Simply stated, the smaller batteries can not deliver their energy at the same high current rate that the sub "C" can and still maintain a normal voltage.

Lixx batteries all have a "C" rating or the rate they can safely be discharged at while still maintaining normal working voltages and without damaging the cells. It is unfortunate that Nixx batteries used for our purposes do not have these same ratings as it would make their capabilities and comparisons between different batteries more clear.

Basic battery 101 really hasn't changed that much over the years but the current demands of high torque servos coupled with more of them in the average airplane has changed making a reliable, higher "C" (discharge rating in this case) rated battery necessary. Thankfully, batteries rated for higher discharge rates are readily available these days and at reasonable prices.

I hope this helps a bit.

Edited to clean up some confusion.