A crossbow is about equal to a musket in terms of the damage caused by a single shot, at close range.
Once you mix in tactics and logistics, the singular advantage departs very quickly. Firstly, a crossbow powerful enough to do real damage in battle was a deceptively complex and fragile piece of equipment. Crossbows were made by artisans. The bow itself was either spring steel or layered bone/hardwood composite; the release mechanism was made of bone for durability; the string hundreds of strands of either fine silk or catgut. Changes in humidity and temperature were detrimental to performance. The bow had to be un-strung whenever the device was not in use, and it could not be stored loaded for any lenght of time. Crossbow bolts were by necessity precise pieces of equiment, fletched carefully to guarentee accuracy bolt to bolt. And they are slow. A fairly powerful crossbow circa 1600 required a hand-cranked winch to draw, limiting rate of fire to maybe 1 shot per minute. All this complexity required trained, dedicated soldiers. Longbows were simpler by far, but required a lot more training for effective use.
When firearms matured as a weapon, around 1640 or so, they posessed positives where archery was lacking. First, a musket is really just a plain iron tube on a woooden stock. Blacksmithing and woodcarving, common basic trades. The flint lock itself is much simpler than it looks, and the parts can be produced in quantity by semi-skilled labor, and later assembled by dedicated armorers. Casting balls out of lead is a much faster and brainless operation than turning and fletching bolts, and a supply wagon can carry a lot more in a smaller space. By 1600, powder was refined to the point where it was stable in transport (corned powder), and coopers made powder kegs by the thousands to keep it dry and potent. Water powered mills could produce tons at a time. DuPont got their start with one powder mill in the Colonial days. All of this is very well suited to naicent industrial practices.
Contrary to a lot of imagination, muskets were easy to use and pretty reliable. By the time a recruit was actually sent out, they were generally able to fire three shots per minute, as per this Youtube videos
http://www.youtube.com/watch?v=SJMbxZ1k9NQ&feature=related http://www.youtube.com/watch?v=Ho-QCmnNMl8&feature=related. Singularily, not much, but when you adopt the tactic of three ranks firing and loading in sucession, you looking at a volley of shots every six seconds. Smoke or no, accuracy or no, that's a lot of lead going downrange. Sure, and individual musket may not reliably hit a horse at 100 yards when you aim at it, but a fifty musket volley every six seconds against a platoon of cavalry, well that changes the odds a little. Finally, maintenance is much easier, really, because once you've fired the musket, all you have to do is clean out the powder fouling, oil the lock and check or replace the flint. No bone release nuts, catgut strings, detensioning bows or refletching bolts.
In the New World, the musket also had advantages over archery for people pushing into the frontier. Versitility. The musket that you were issued for the militia could come home and put meat on the table, ball for big game, small shot for fowl and small game. It could be left loaded and unprimed on the wall to be ready at a moments notice to keep the preadators out of the cowpen or brigands out of the stable. Big and awkward compared to a modern weapon sure, but anybody from 12 years up could use it effectively, if need be.
Probably missed the whole point of your initial post, but it is Friday night and, boy, we brew some good ales in Wisconsin. Cheers.