I found this.

historically, the longbow had longer range and a dramatically higher rate of fire than a crossbow. the only advantage of a crossbow is its simplicity and ease of training (hence crossbow militias), and the fact that it could be carried cocked and ready to fire.

a crossbow militia in the game should represent civilian tradesmen, merchants and farmers garrisoning a city/town with crossbows. english retinue longbowmen are elite archers whose sole purpose in life is archery and war.

a well trained professional crossbowman (without assistance) could fire 3 shots per minute. a militia crossbowman probably less.
a professional, experienced longbowman was expected to shoot 20 shots per minute.

in the game, crossbowmen have about 2/3 the firing rate of longbowmen (wtf!). set up at max range, militia pavise crossbowmen will (most of the time) inflict more casualties on retinue longbowmen - even with their slightly slower rate of fire. when the retinue longbowmen run out of arrows the crossbowmen still have about a third of their arrows left, which they can use to inflict even more casualties. the only way the retinue longbowmen win is if they close to very close range and/or if they charge the crossbow militia. this is unrealistic.

even with 2 servants and 2 crossbows (one to hold the pavise, and one to reload the second crossbow), a professional mercenary crossbowman can hope for up to 8 shots per minute. the pavise crossbowmen in the game have no servants, are militia civilians, and only have one crossbow.

in the least, crossbowmen need a nerf on their firing rate. its rediculous that not only do they have much better defense, the armor piercing stat, free upkeep, low upkeep when not garrisoned (100), and the ability to be recruited from just about any city, but that at range they can inflict more casualties than the professional, elite english longbowmen. either that or professional english longbowmen need to have their attack speed doubled.

from Ambrosiuss (tw center)