First of all, a AA cell is the same size as a 14500 not a 14650. Next, Compare the power of each cell, a AA has a usable voltage of 1.6-.8V and a 14500 4.2V-3V which means the nominal for each is 1.2 vs 3.7V so multiply those by the Amp hours for each and you get 2.5 X 1.2 = 3 Whrs vs .8 X 3.7 = 2.96 Whrs. So a primary cell has a slight edge in power but alkalines can’t drain quickly without a major loss of usable power. At anything over 100mA draw the 14500 will be superior. Nimh cells have much higher drain rates but boost drivers for small lights are still limited to ~1A and even that much led current will draw close to 3A from a nimh cell.
For that particular light it boils down to the driver not regulating both cell types to the same current. The AA needs a boost driver and the 14500 is probably pushes it into direct drive so you’re not comparing apples to apples.