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I reckon you may be right.
The eTrex 20* use both GPS and GLONASS, it last a lots longer because of the battery (2x AA), I managed nearly 2 days out of it before the battery fully depleted and that include leaving it on at low brightness all night, if I use rechargeable battery on the eTrex, it might last as long as says the 810.
*screen resolution is very similar to 810 apart from the lack of touchscreen.
It's different circuits though ain't it, so it's effectively running two GPS circuits (maybe). I still say it's the screen that chews the juice.