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Cannot say I have noticed a great deal of difference as opposed to using the map , if anything I would say it is less power hungry than when using the map but the difference is small and may be due to other factors.
With regard to batteries having used some eneloop pro rechargeables for a few weeks I am very impressed with the battery life. After a six hour hike the battery indicator is still showing full I used the compass pointer for this.
Does it drain the battery a bit using the compass?