If I recall correctly, the break even point between Alkalines and NiMH (rechargeable AA's) is about 350ma; for a device that draws less than 350 milliamps (.35 amperes), a quality alkaline will last longer. Great for low-power (5mm) LED's and remote controls. For applications above 350ma, such as power LED flashlights, portable stereos, and the like, NiMH's will last longer. For Li-Ion cells like 18650's, this difference is even more pronounced. Some high-power XML flashlights, such as the Fenix TK21, have been known to overheat lithium primaries (CR123's) while happily taking 18650's. Most (reputable) 18650's are able to discharge at twice their rated A-h number. That is, a 2400mah battery can discharge safely at up to 5A (which can drive 2 or more XM-L lights to pretty high levels). The cheap 18650's sold on DX and similar websites of ill-repute are known to be refurbished laptop cells and other used products. You will likely not get good performance with those.
Also, Li-Ions can have much longer service lives than rechargeable AA's when frequently recharged; that is, if you only run them down for an hour or two (such as on one commute) and recharge them that night, you can get the equivalent of thousands of cycles, while NiMH's wear out almost regardless of how much they are discharged. Recharge early, recharge often (or, get a dynamo for everyday lighting)