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Some says its finding satellite quicker thus less time searching, others adamant that it drain battery more having two system running.
The latter. More satellite signals mean more computation required which means more battery drain.
The time to initial lock of modern GPSes has been improved in lots of other ways (especially with the bluetooth/WiFi GPSes that download up-to-date ephemeris/almanac data rather than waiting to get it from the satellites themselves).
There was a fairly big discussion on this topic earlier about GLONASS actually and whether it eat more battery or not.
Some says its finding satellite quicker thus less time searching, others adamant that it drain battery more having two system running.
IMO, it's the screen that drain the majority of the batteries.