Nope, using current phones, black background, white text uses more power than the converse, although it’s probably not measurable.
Slightly simplified explanation follows:
Modern active matrix LCD screens have a constant illumination from behind, which is where all the brightness comes from. If you’re looking at totally black screen on your phone or monitor, the backlight is still shining, it’s just completely blocked because every pixel/filter of every color has become opaque. Opaque being the charged state. To display white, it’s the opposite. The individual pixels are not charged, and the backlight shines through unfiltered appearing white. To display blue for example, the red filter and the green filter are charged allowing only the blue to show through. Purple, only the green filter is charge to block the green light, you get the idea.
See, now with white text on black background, you’re actually using more power, because there is more background than text. Now it’s irrelevant, since your power consumption for your display is almost completely backlight with less than 1/10 of 1 percent being the actual LCD crystals which are very efficient. Still, there is nothing to be gained power wise by using white letters on a black screen.
Thanks. Though not getting bad attention in the theater would be a gain. I’d love not to have that blaze of light on my periphery. I’ve seen some people text all the way through a movie. “Oops, I’m sorry I stumbled and spilled my jumbo Coke all over your phone!”