Crossbows vs. Longbows

[Lingchih]

So, something that has always bothered me. Crossbows are armor piercing, while Longbows are not.

Don't get me wrong. I have never been in a crossbow or a longbow fight, but the Battle of Crecy was won by longbowmen zinging the French Knights to death, right?

Crossbowmen were generally poorly trained troops who could crank a handle, and shoot quickly without much training. Longbowmen were highly trained veterans, who could shoot with amazing force. I believe the longbow hit with much more force than the the crossbow.

So, why are Longbows not armor piercing?