[BigDaddy]

Crossbows use a mechanical advantage to pull back the string. Even the ancient crossbows seem to have higher kinetic energy, because of larger projectiles but has a slower projectile speed. So, theoretically, they could penetrate armor better.

I've learned a bit since this discussion started. The problem appears to be that both bows did what they were designed for well. Both pierced armor, and if the longbow didn't, they would just use different arrows. In the time period prior to 1500-1600 or so and maybe after that longbows outdistanced crossbows considerably... although, it appears that even this may have been largely due to crossbow users being essentially unskilled archers.

The lesson seems to be that you need several times as many similarly skilled crossbows to be as effective as longbows would be. Because crossbow archers were frequently unskilled, you would need many more, and even then you might have, at least, range problems.

And range problems in such situations are pretty severe and can have telling consequences.

And also, regarding the Catholic Church 'banning' the crossbow, it seems that many people think that was a law regarding dangerous shooting exhibitions. As I don't have a copy of the law (and couldn't probably read it if I did), I can't give an actual opinion as to the nature of its intention... So, I assume it was a common law designed to keep reasonable and decent order.