I would have assumed that the crossbow was much more deadly. When you think about it, its like a primitive gun. It's as simple as point and shoot, whereas archery takes much talent to be decent at. Why were the English longbow men so dangerous and not, for example, a French crossbow?
Please take a look at the FAQ section on the longbow, with great contributions by u/MI13, u/Hergrim, and u/Valkine. In summary to the question, at least by the late Middle Ages, the longbow wasn't really all that deadly. Longbow men were dangerous because their archery disrupted formations and impacted morale, and after running out of arrows they could join close-quarter combat, and that there were a lot of them.