Higher brightness LED with bigger resistor to save battery life
Other things being equal, so the same battery voltage, running high brightness LEDs at 5mA will use less power than running standard LEDs at 20mA. 

In each case, if you are controlling the LED current with resistors, then you would use larger resistors for the lower current.

In each case, your efficiency would be the LED voltage divided by the battery voltage.

If you have a much higher battery voltage than your LED voltage, then you could improve efficiency by using a constant current output SMPS, instead of a resistor. However, resistors are cheaper and simpler.