Originally Posted by
Silent Assassin
As other members mentioned it depends on a lot of things, the first and most important one is which faction your are playing with, for example if you choose Milan, their Genoses Crossbowman are extremely powerful and they can recruit them early in the campaign. See below the ups and downs of each:
Archers:
Some may deploy stakes (England higher end archers, Turks Jannissary archers, etc...)
Longbowmen get the armour piercing bonus
They can use flaming missles
They shoot faster then Crossbowmen
They use plunging fire, so can fire over other troops and walls
Crossbowmen:
They have Armour Piercing bonus, this means in late campaign they are stronger then archers
They are better in melee then most archers
They have a better defense as they have the shield bonus and can use pavises
They use direct fire, so can only fire from walls up to a certain distance, and don't find it so easy to shoot over terrain or other troops