I agree that the rate of fire for the longbow should be significantly greater than crossbow units.
English longbowmen spent years (from childhood) practicing their art, and could loose anywhere between 13-18 arrows a minute... and these were aimed and accurate (distance-wise). The range of the longbow would have caused chaos at a distance (and death for lighter armed troops) and utter slaughter at closer range.
The crossbow was largely useless at long range. It couldn't fire effectively in an arc which meant it was only really effective at less than 100 yards.
Both the longbow bodkin and the crossbow bolt were lethal at close range, but the skill and accuracy of the longbowman combined with his rate of fire would mean a longbow unit would make mincemeat of a crossbow unit - pavice or otherwise.
If M2:TW was more accurate, it would cost more to build longbow units (to reflect the training required) but their upkeep would be low.
Crossbow units would be cheaper to build, but cost more in upkeep.
In a standoff fight the range of the crossbow would be at least 2 times less (probably more) and the rate of fire at least 3 times less.
The Longbow is the English superweapon. While it's useful in M2:TW it wouldn't instil the same level of fear that the real weapon did.
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