The sling sites where sited earlier, after saber cherry asked for them.
Here's one of many comparisons showing a typical xbow vs a longbow.
I found it by typing:
longbow crossbow
into my search engine. I read the same thing repeatedly in my search to prove crossbows superior. If you look, you will too.
http://www.thebeckoning.com/medieval...oss_l_v_c.html
The draw length IS VERY IMPORTANT. I won't go into this in length, its covered on this site and many others. With much less draw stregth current crossbows fire quarrels 2-3 times faster (138fps to 320fps). Hee hee, I said V-shape (meant U shape). A medeival xbow is like ")" a modern crossbow is like a "U".
Scopes and sights are only important for accuracy, so you're right the heavy crossbows must not have been widely used for some other reason. Though the one on the quoted sight is 740lb draw (suspect).
A crossbow, it seems, can penetrate armor at somewhat longer range.
Did I miss anything?