The plot shows voltage across (yellow) and current drawn
[1] (white) by my eTrex 30, powered via its USB port for convenience (no battery in the unit). X axis is one second per division.
Spot the point where I turned the GPS reception off entirely ("demo mode" on the eTrex)...
It's the slight peak just before the midpoint of the graticule. The slight increase in current around that point will be due to rendering the menu.
For comparison, here's the backlight going from 0% to 100%:
And here's the map being zoomed from 200m out to 8km:
Next, I tried to measure the effect of the rate of track logging. I set it to log a point per 99 hours, with the GPS on, and left it on the menu screen to avoid map rendering effects. Once it had settled to a steady state it looked like this:
I then changed it to record 1 point per second, and again let it settle. No observable difference.
In summary then, the backlight uses a substantial amount of power (dwarfing all other effects), as does processor-intensive map and GUI rendering. The GPS receiver itself doesn't seem to affect current draw, either because it's never actually switched off, or because its draw is negligible.
So in terms of battery life, it's mostly about the backlight, and map rendering.
[1] Don't read too much into the exact current measurements, I don't have a precision shunt resistor to hand. They're somewhat high.