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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.
For the amount of DPI and brightness the screens outputs, it has to be. Might try a full power/ no GPS power down test between the 810/1000 at work and see how they fare.
There's also very little info about Garmin internals it seems. Would be interesting to see what chipsets are used.