The lower voltage may greatly reduce current. (voltage on resistor = Battery voltage - Diode forward bias* N … )… hence extending life.
Actually the amp hours of the batteries are all fairly similar, if used for low currents, but for high currents, the more expensive formulation lasts longer…
The drumming bunny is a high current application, so is the digital camera or incandescent torch…
LED’s are meant to be low current ? Sure the expensive batteries may last twice as long, but they cost 10 times the price !