That was my initial impression as well. However, a battery's ability to source current is often measured using a C-rating that is based off of the mAh. Many batteries have a 1C rating and would then be able to produce 1A of current (with a 1000 mAh battery). A larger mAh battery with the same C-rating will be able to produce more current (2000 mAh at 1C is 2A). So, if the C-rating is constant between two batteries, the larger mAh battery will be able to deliver more power. I'm a bit new at this so maybe I'm getting it wrong, but that is my understanding of the subject.
That's true for the most part. If no one fidged on the mAh rating, I was initially talking about the ops question to voltage. Take AW vs the Fires in the same size. The Fires will usually be STAMPED with a higher mAh rating. The flashlight forums have done lots of test on these and it's pretty much came to the conclusion across the board AW is rated truer and will preform just as good or better in amp load test. Then we have IMR vs Li-Ion, at the same size the IMR will usually have a lower mAh capacity but a higher c rating.