Does a white background eat more battery?

Very unlikely, normally what eats power when it comes to displays is the backlight.

Ofcourse, it needs more power since a constantly pulsed electric field needs to be applied to the white LCD-pixels.
However, i think the difference in battery runtime really is neglectible.

With this display technology, white vs black backgrounds don't make any difference. I believe it's called something like "memory in pixel', where power is only really used when a pixel changes.

With this display technology, white vs black backgrounds don't make any difference. I believe it's called something like "memory in pixel', where power is only really used when a pixel changes.

It simply consumes less power, but it definately does permanently - not only on changes.

But no difference with a black bg vs a white one.

No, because no matter if the memory circuitry is integrated into the pixel or not, the liquid crystal molecules need an electric field to maintain their state opposit to the powerless state (twisted/not twisted).

Black pixels are the powerless state and thus need no electric field to be applied.
So a dominant black screen should consume less power than a dominant white one.

But as said... i don't think you will see much difference in battery life.
Much more relevant is what the software is doing.
Does the screen need permanent update (seconds displayed, pulse displays etc.) and thus is the "awake" time of the CPU higher and so on...

Interestingly Garmin doesn't even mention "selecting a black background" in their post Maximizing Battery Life, so Forerunner is probably correct in stating that the difference is negligible. I did a bit of testing on my tablet where there should theoretically be a significant difference, and I couldn't see any. But I would be curious to hear if anybody has run actual tests on a Garmin watch. 

So in my case it’s 3 times as much: I recently discovered benefits of white background making numbers much more notable to my eyes while sitting at home office in cloudy Germany ...

i switched a face called Shariot J-Shock and tested my hourly consumption in a “silent mode” (no notifications, gps, etc.).

while the face is quite populated, it appealed to me due to extremely fast and low power cons. parameters. But! The moment I switched it to white mode, it started eating 0.3-0.4% per hour instead of 0.1 previously.

so yes, I see a big difference of a factor of 3 between white and black background.