The crossbow was a great advance in medieval warfare, but it was not the be all and end all of archery. The main benefit of a crossbow was not its armor piercing ability, but that any peasant shanghaied out of his field the morning before could learn to use it. The only trick is learning to estimate the range to your target. The longbow requires much more training and discipline to use effectively.

The longbow can fire about 3 times faster than the crossbow, and is more efficient. A medieval crossbow with a 740 pound draw weight fires bolts at the same velocity as a longbow with a 68 pound draw. Because the crossbow has such a short bow compared to the longbow (that's probably why it's called a longbow, huh), the tips of the bow don't reach the high velocity of a longbow. The velocity at the tips of the bow translates directly into velocity of the arrow (or quarrel, as they call crossbow arrows). Thus to reach the same velocity as a longbow, the crossbow requires much more force in the bow (and therefore a higher draw weight). This difference in efficiency is much less with modern crossbows made of high-tech materials that can withstand the stresses in a 780lb bow, but was an important consideration in a time when bows were used in real warfare.