[Omnirizon]

i've actually done some light research on this topic as i prepare to add these items, alongside firearms, into the Fourth Age project.

Longbows:
less force
higher rate of fire
years of training required

crossbow:
more force
lower rate of fire
weeks of training required

firearms:
terrible aim
dangerous
cheap
little to no training required. the weapons had such poor accuracy there was actually no point in training marksmenship. all soldiers needed to know how to do was to prepare the weapon to fire and to move in the correct formations.

i've read that firearms were actually cheaper than crossbows, which is the another reason they were used, other wise they were worse in every capacity (except for low train time).

the ammunition required for the weapons was another reason firearms were used.

longbows:
fletching requires skill and is expensive. it may take weeks to produce a bundle of war worthy arrows.

crossbows:
bolts require less skill and less money

firearms:
shot required little skill and could be made quickly for very little money. soldiers could actually produce their own shot in the field if necessary.

lastly, their were environmental factors.

longbows:
wind could easily cause stray arrows

crossbow:
with more force, wind was less of a factor

firearms:
wind had relatively little effect on firearm shot. additionally, the accuracy of the weapon itself was so poor a little straying didn't matter at all. additionally, all the smoke would foul cavalry charges a little. however, in the rain the weapons were little more than clubs.