Note: It's hard to say which of these two weapons is "better" because they both have their advantages and disadvantages. The longbow generally has a greater range and is faster to load than the crossbow, but the crossbow can be used by almost anyone and has more armor-penetrating power depending on the distance to the target, the size of the bow and other factors.
According to various sources I've found, a longbowman could shoot around three arrows in the same amount of time it took for a crossbowman to shoot one. On the other hand, the crossbow didn't require as much strength or training and the wounds it inflicted were so terrible that its use (against Christians) was banned by the Second Lateral Council in 1139. (Wikipedia)
"IN THE 12th CENTURY, the crossbow was considered by many to be a weapon of mass destruction. Not only was it was remarkably accurate and deadly at vast distances, but shockingly, the bolts it fired could penetrate a knight’s armour. Crossbows meant that no breast-plated nobleman, prince or king was safe on the battlefield. Any low-born peasant with just a bit of training could kill a lord or sovereign with simple squeeze of a trigger — a platoon of crossbowmen could wipe out a kingdom’s aristocracy with just a few volleys ... And that was something Medieval elites feared might shatter the natural order of society." Source: Military History Now.