Right, I'm just wondering if anyone has had a noticeable difference when using the white background.
Personally, the white looks a bit meh. IIRC, the 928 uses a Pentile display, so they tend to be a bit cooler than the RGB displays (white looks blue/greenish.) The colors pop better against the black too.
Anyway, it's tough to test properly because the background doesn't just affect the start screen, it also changes to colors of apps and the various menus. A white background will absolutely eat your battery more for the reasons stated above (black pixels in an AMOLED display draw no power), but it really depends on what you're doing as far as how much. You could fully charge the phone, and then perform a specific set of actions (let sit on home screen for 15 minutes, go into the settings menu, let sit for 15 minutes, go into an app, let sit for 15 minutes, etc) and see how much it drains. Charge it again, and repeat with the other background and see how it does. Put the phone in airplane mode to stop radio hunting from eating at the battery.
Either way, if you can get through the day with 50% or better of your battery life remaining, I'd imagine you wouldn't have any troubles with the white background.