To pinpoint one difference I love:
In FitD games the basic mechanisms for action are more consensual than in PbtA games. I’m BitD, consequences are known (or mostly known) before the roll, whereas in PbtA there is an element of surprise to failures that has its own highs and lows.
One result of this: GMs have the opportunity to flirt with failure in FitD games, even if that roll is ultimately a success.