Looking at your thought experiment, the difference is whether that customer gets $500K (all of the bank's assets are sold to make him whole[1]) or $1M - all the banks assets are sold, and also he gets another $500K from the FDIC.

[1] - the $250K insurance is normally only supposed to apply if there are insufficient assets to cover it. Unless I'm misunderstanding your wording and the bank in the thought experiment has $750K in assets.