[Kamamura]

One quick note - longbows, unlike crossbows, were used as an indirect fire weapon in battle (firing in high arc, the arrows coming from above). As such, it was much more difficult to take cover from them.

On the other hand, crossbow bolts from heavy crossbows were fired with terrible force - contemporary sources say they could pierce an armored knight altogether. The fact that the Pope issued a bula forbidding Christians to use crossbows against each other only prove, how feared weapon it was.

I think the composition of troops was also mainly determined by regional tradition - in England, archery had long tradition and therefore the populace supplied large numbers of bowmen. In real life, you cannot just "build" archers for money as in most games. The only game I know that reflect this is Crusader Kings - your nobles bring their subject to fight, and the troop composition depends on the social classes and terrain of the province, and you as a king can't influence it.