The amount of light produced is determined by the watts the led consumes, and the efficiency of it (and some other factors).
If you connect a led without driver, it will only light up if the battery provides around 3,7V. Thats a li-ion, or three alkalines (4,5v) or NiMH (3,6v) in series. The current draw here will depend in many factors, like the internal resistance of the battery, the kind of led, the kind of cables.. etc..
NiMH has very low internal resistance, so they can give a lot of current without beeing damaged. If you try to draw a lot of current from an alkaline, it will be damaged (internally) and will not give you all its power. Thats why some NiMH in series are used for high power leds.
If you are powering a flashlight with an XRE R2 led, with 1x18650, it may draw something like 1A on high (3.7W of power). If you use two 16340 in series, it may draw 0.5A, because they are 7.4V in series, and if the driver is good, it will give you the same power: 3.7W = 7.4V*0.5A.
Be careful because every driver is different, some of them will burn up if you provide it more than 4.5v.
When people say that a flashlight draws X amperes, most of the time they asume they are using 1 li-ion cell (3.7V), in any other case they specify, which configuration they are using.
If you use one AA (and the driver is good), it will try to draw a lot of Amperes to compensate the low voltage of it. NiMH are capable to last more time with higher current draws than alkalines.