When you say 10% duty cycle, you should specify that the duty cycle refers to the voltage applied. everything else remaining same, 10% duty cycle shall result in 10% average brightness. The average should be calculated over a complete cycle under steady state.
effectively, LED output is proportional to instantaneous power input (approx). This linear relation is often used in opto couplers.
I do not see how LED pulsing can lengthen battery life. It can, if (say) you turn on the LED 10% of the time (but not at high frequency). In that case, the average brightness is low (because it is off most of the time) but the status is visible (because it turns on often). In such cases, the LED is being used as a status indicator and not a source of illumination.