It has to do with the level of current draw. Alkalines are usually rated at higher voltage, and under light current demands will maintain the higher voltage.
As power demands increase alkalines suffer more voltage drop than NiCad or NiMh rechargables, so at higher power drain levels rechargable batteries can actually end up delivering higher voltage and current.
Alkalines start out at 1.5v, but under heavy load can drop to 1.1v or less. NiCad and NiMh batteries start out at around 1.3v, and will typically maintain 1.2v even under very heavy load.
This is why alkalines work better in low current demand devices like radios, clocks, remotes, etc., and rechargables work better in high drain devices like digital cameras. (And why you can take a set of "dead" alkalines from a digital camera and put them in a radio or remote and they will work fine - they've still got plenty of power, just not enough current capacity.)
As far as flashlights are concerned, it all depends on how much current at a given voltage the light demands. For example, if your light is running 4 cells and a 5 to 6v lamp, then rechargables won't deliver maximum brightness because the voltage required is more than the typical load voltage of NiMh batteries (1.2x4=4.8v). On the other hand, if it was say a 4.5v lamp that was hungry for more than an amp of current, then NiMh would be the better choice, since under that kind of load they will still deliver enough voltage, while alkalines will usually choke.
The "break even" point is not an exact number, as different battery brands and variations in chemistry will affect performance.
All of the above is based on unregulated lights. Electronic regulation circuits found in many LED and all HID lights will compensate for different battery types and you will find little if any performance difference in regulated lights (at least as far a brightness is concerned).