Hmm. I'd be interested in seeing your source for that. Yes, the power imparted to the arrow is the integral of the poundage supplied by the bow or prod, over the distance that it is propelling the arrow, and that distance is shorter on a crossbow than a longbow. But you can have a much higher poundage and still be usable with a crossbow; you have two arms to draw together, and are supporting none of the draw weight while aiming. I've seen the analysis of draw weights of longbows on the Mary Rose; do you know where there are sources for that of crossbows?
And yeah, sorry, I didn't mean to make it sound like they were just handing out longbows. Longbows do require significantly more training. In part, the tradeoff for longbows is that you have cheaper weapons but need to put more into training the archers.
Payne-Gallwey's "The Book of the Crossbow" is at least in the same category as the paper's cited "Great Warbow". At one point he tests a 15th century siege crossbow with a draw weight of 1200 lbs, which is probably close to the upper limit (and requires a heavy cranequin). IIRC the Mary Rose longbows were about 150 lbs.
But that's a steel bow, which is stiffer than wood, and the draw length is pretty small.
W.F. Paterson published a test that compared a 70 lbs bow with a 740 lbs crossbow, and the initial velocity was about the same.
Now how that equates to actual damage is another issue, and I haven't seen a really good test about that. One major factor that one has to consider is that damage varies with range, too. So what might look comparable at close range might be completely different at far range. (I think the Genoese were out-ranged by the English at Crecy.)
And yeah, sorry, I didn't mean to make it sound like they were just handing out longbows. Longbows do require significantly more training. In part, the tradeoff for longbows is that you have cheaper weapons but need to put more into training the archers.