A great question and there is your reason. Gunpowder may well have been weak, but a slug or even a charge of nails would do great damage in close quarters and obviously they were able to hang onto this against its recoil.
The cross bow is operating at medium range and this would be closer targeting armor. It would also be excellent in support of pike-men against heavy cavalry.
Except with the English, the long bow was not often deployed, and its advantage was in range. It could imposes rapid plunging fire on a charging body of men. I actually do not think that the long bow was ever fully exploited. In combination with a pair of horses, the second carrying a bundle of arrows, you have the capacity to close on a group and hurt them at a substantial distance that would be comparable to Mongol ability who used a smaller but stronger bow....