Cost of material, usually! The black background is more expensive, but the white one can be screen prined cheaply if necessary.
Though it would be nice to think that 111's is on a white background because it showed up better on black flying suits from their Black Arrows' heritage, I fear that would be bull$hit!
Oh - and don't call them 'crests' or you'll upset the Chester Herald. They are, in fact, 'badges'!