It could take years for a longbowman to become sufficiently trained, whereas the crossbow's simplicity of use made it suited to even the basest peasant, so long as he didn't point it at the wrong people. More expensive to produce, perhaps, but the lesser amount of money it required to use grossly overbalanced that.
Crossbows applied so much force to each bolt (between 400 and 600 pound draws), that they necessarily required great amounts of force to draw. Men are only so strong, but as time went by, innovations were born, and soon there were stirrups in nose, and hooks on men's belts, so that to redraw the bow they needed only to bend down, insert their foot in the stirrup, and draw the cord back with the hook as they straightened as we see in Mount and Blade.
Also when you think about it a longbowmen would probably fire at the horse and not the knight.
Most horses weren't armorer due to the size and diffuculty of getting an accurate measure.
There is no doubt that the circumstances determine which weapon is best in every case, but I would think that the range of the longbow would make it better suited for ambush, where the element of surprise might make up for the lesser stopping power; it is also my personal belief that, while the crossbow took somewhat longer to reload than the longbow, the rate was still high enough, especially later on, to make it aptly suited for pitched battles, where the knowledge that crossbows were in use might also be used as a weapon. A longbow would be bulky in an ambush with lots of brush and trees. A crossbow is easier to manuever.
t was really rather saddening in how a knight with years and years of training could be killed instantly by a peasant with one day's experience with the crossbow. It seems, though, that the death of sophistication and pride is a side effect of progress: technology and its limitations are the bane of specialization and customization.
The Crossbow is much more accurate and stronger then the bow, it lets loose a very powerful bolt. However, the bow can fire much more rapidly, and in a large group it would be much better to have 30 men with bows, firing 6 shots a minute inaccurately then have 30 men with crossbows, firing at the most 3 shots inaccurately a minute.