Had a look at some battery tests, to exemplify my point of a higher capacity rating not necessarily equaling more useable capacity.
A comparison between the high drain Panasonic PD/PF (2900 mAh) and the highest actual capacity 18650, the 3400 mAh Panasonic ncr18650 (from dampfakkus.de):
At a 5 amp draw the pd/of has more capacity from 4.2-3.2v.
At a 3 amp draw the pd/pf comes out on top from 4.2-3.3v. At 3.2v (at which point most apvs have already cut out) the pd/pf has 2425 mAh compared to the other's 2531 mAh.
At a 2 amp draw the pd/pf has more capacity from 4.2-3.7v, and only starts to lose significantly at 3.3-3.2v.
The higher drain Sony vtc5 (2600 mAh) and LG he2/purple Efest 2500 mAh clearly win at a 5 amp draw. At a 2 amp draw the Sony and LG/Efest clearly win from 4.2-3.6v and only lose significantly at 3.3-3.2v.
So, higher mAh rating really isn't the criteria you should choose your
batteries on, even when the stated mAh rating is (fairly) accurate.
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