I would prefer shutting the screen off- Flashcarts consume enough battery already.(In alpha2 fix4)
When I launch Super Mario Advance 2, is bottom screen is white (which I assume is correct).
When I launch Yugioh Dungeon Dice Monsters, the top screen is white.
As for the white screen, I would personally prefer just shutting off or blacking out the unused screen.
Shutting it off would save battery, whereas blacking it out would be less annoying.