Actually, some papers written about crossbows seriously doubt that the penetrating power was that much better -- if at all. The poundage certainly was, but it had to be -- crossbow arms are short and the arrow doesn't travel as long, thus less time is available to transfer energy.

And "large populace" makes it sound like they just handed out crossbows to peasant levies, instead of them being very highly paid mercenaries. I mean, I can hand a bill or halberd to a peasant, too, but that didn't stop the Swiss from getting hired by most of Europe...