First of all, if you need to measure runtime you must provide a clearer definition of runtime. I understand it basically can be defined as “the amount of time the flashlight remains powered from switch on until condition”, thus you need to define condition for runtime measurement (battery voltage, amount of flashlight output, etc.).
With the above in mind…
Using a boost-buck or a boost driver it is easy: slight increase in runtime. Switching drivers usually have well defined cell voltage windows and a boost-buck or boost driver would be able to run the emitter at the condition specified power/current from full battery until cut-off. With a buck driver, at some point battery voltage would get close enough to the emitter Vf as to force a reduction in driving current / emitter power. With a lower Vf emitter the regulated window is larger (coupled with a little bit higher efficiency), so runtime at selected current or emitter power is larger. However, high Vf emitters (slightly less efficiency) also cause the driver to stop switching operation and reduce current and power sooner, this means the runtime would be larger in this particular case for a high Vf emitter (if condition allowed); and thus, comparatively speaking the low Vf emitter would have less runtime (with these conditions) because of a higher runtime window at full power.
With linear drivers (regulation using MOSFETs as variable resistors) a low emitter Vf reduces runtime, this is because the window at which current remains constant (battery voltage > emitter Vf + other component voltage drops) enlarges (causing higher average battery drain), so the amount of regulated time is larger but total runtime gets reduced. Regulated time is a fraction of total runtime, by the way.
With unregulated MOSFET drivers the answer is @#$% easy: less runtime. This is because the larger the difference between battery voltage to emitter Vf, the more the driving current (and emitter power, lemons, etc.).
Note: had to edit this more than once. If you find something worth being corrected, say so. Thanks!