so here's the pics:
It's hard to see the difference, but look closely, the light box on the right is brighter, and has more even distribution.
So the naked eye is the only measuring device here, since that's what's going to observe the actual brightness anyways. I don't have any fancy equipment, this is just a proof of concept. It seems the difference is slight, but this is a small scale example.
The winner is white (box on the right), it's just a little brighter, and more even. If this were done with actual LEDs in the scale biggy is planning, I'm sure the difference would be more noticeable.
So, biggy, it's worth the extra time to paint it white. (even if it's only for a few extra nits.) If my test is wrong (and every single LCD manufacturer too) then it will only be darker by a few nits. There's not really much to lose here.