[Dhaeron]

Wee! Can't resist keeping this thread alive. (And it was about time to finally post something here after lurking for years)

I've been doing archery as a hobby for while a while so i hope i'm somewhat knowledgeable about the subject.
The big problem with using a strong bow is not so much aiming (which works very well) or learning how to use it, but to build up the muscles needed to use it. Despite the claims of many computer and PnP RPGs (whose creators probably never touched a bow in their lives) using a bow repeatedly requires significant muscle mass and enormous stamina. Shooting a 100lb bow is pretty much like lifting 100lb barbells, with one arm, repeatedly. And Under battlefield conditions the proverb was: Accuracy is nice, but go for volume. Shooting ten or more arrows a minute was desirable. But go ahead and try that with a bucket of water and see how often you manage until it feels like your arm falls off.
It takes months, or even years of training to build up the kind of stamina needed to keep shooting for more than a very short time. Shooting with a reasonable degree of accuracy can be learned in a few days though.

A crossbow on the other hand can be used by anyone, anytime.

Another fun fact is that medieval and ancient crossbows (the greeks already used them) reached mostly the same projectile velocity as bows, mostly because that's limited more by the materials available for the arrows & bolts, than by the materials available for the bows & crossbows. A big part of why compound bows can have stronger pull is that they increase acceleration over time, putting less strain on the arrow.
Since crossbow bolts are shorter than arrows, they were generally lighter in medieval times, making them overall perform worse.
With modern materials crossbows can easily outperform bows, and it can be possible with medieval materials as well, but people didn't have the knowledge of physics back then to design them that way.