Thanks guys. But what is the consensus here? I know nuts about batteries.
There's a thread floating around here that talks about voltage of a cell for a given current draw, but I can't seem to find it.
In a nutshell, the 3100/3400 mAh cells have a slightly different design that gives it more capacity. The drawback is that when the cell is under high current draw, the voltage of the cell ends up being lower than on a 2600 mAh cell given the same current draw. Because of this, the driver must draw even more current from the battery to maintain the current draw at the led. It's this lower voltage/higher current demand at high current draw (i.e. lower efficiency) that makes these 3100/3400 cells not last as long as the 2600mah cells under high demand.
At what point this becomes true, I'm not sure, but I don't think 2.8A is it. You should get more runtime with the 3400mAh cell with this light.