[Panpiper]

As I understand it, what causes the seeming discrepancy of crossbows being armor piercing while longbows are not while having longer range, is the fact that the crossbow bolts are heavier. The heaviness of crossbow bolts reduces their ability to stay aloft but at the same time gives them a greater impact, hence their ability to pierce armor. Longbows could indeed pierce armor, but they were also greatly helped at Agincourt by being fired from a higher elevation, so the extra drop lent them velocity.