When archers aim for headshots, and while crossbowmen are reloading, they miss mostly. And unlike archers, crossbowmen get high precision in the battles and mostly fired bolts eventually find a target. And they are really ahead because of long range. Compared to Fian Champions, they start firing in the beginning of the battles.
And one point I want to emphasize is that, I don't know if you've experienced it but crossbows AI is better imo because they really select the targets in skirmishes.