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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.
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Compasses cost virtually nothing in terms of power, the chips are cheap their signal is easy to read. Usually they're not even read constantly, an accelerometer is read to constantly adjust the compass which avoids even asking the fractionally slower chip. The accelerometer is essentially free to call. The compass is only queried periodically to ensure that the accelerometer hasn't caused any drift in value.
All-in-all... compasses cost nothing.
Having the screen powered... costs almost everything.
On the etrex i find it easier using the direction arrow as opposed to the map. i.e it should always be pointing in the direction you need to go.