In Empire of The Summer Moon, a history of the Comanche people, CS Gwynne says that the the bow and arrow was more effective than rifles until it was eclipsed by the invention of the six shot revolver. But if that is true, surely European armies should have been using bows instead, right?
Hi, you may be interested in further discussion - from the FAQ:
####Transition from Bows to Firearms
The effectiveness of weaponry all depends on context. Even certain modern militaries and police forces - notably the PRC and Taiwan - still employ crossbows among their SWAT arsenals... for much the same reason that Daryll from The Walking Dead finds it such an effective weapon in the post-apocalypse: it's about as powerful as a rifle, and much, much quieter.
But as to the meat of your question, why did most armies rapidly shift away from archery and to firearms? It's not that they were really better - certainly not at first, as early firearms were slow to reload, and difficult-to-impossible to aim with anything resembling accuracy until rifling came around. Meanwhile an experienced bowman could fire off as many as 5-6 arrows per minute (vs. 2-3/min for muzzle-loaded weapons), and among the more elite ones such as the Mongols and the Plains Indians, supposedly with accuracy sufficient to hit a bird in flight from the back of a galloping horse (though that seems a dubious claim, to be sure).
So why switch over to an inaccurate, slow weapon that immediately gives away your position and often has technical problems like jams and misfires? There's a couple of reasons:
First off, Training: It's much easier and faster to train a soldier how to load and shoot a rifle, than to teach them how to be a proficient archer. The fact of the matter is pretty much anyone can point and shoot a gun, whereas archery requires both mental and physical training on the order of years to develop proficiency. This becomes of critical importance to Europeans when conflicts like the 30 Years' War breaks out requiring rapid deployment of massive conscript armies, the size and scale of which Europe hadn't seen since the likes of the Roman Empire a millennium prior.
Then there's Ease of production - Sure a rifle has more moving parts and is more technically complicated in a mechanical sense... but they can be mass-produced using standardized parts. This has two advantages over bows: #1 they do not require special-grade material such as single high-grade wood of sufficient length (such as the yew wood for English longbows, for instance). In a pinch, a rifle can be made out of almost whatever scrap that's lying around. #2 when.if a component of the firearm malfunctions or breaks, it is often possible to simply replace that part, rather than crafting an entire new weapon. That's impossible with a broken bow.
So, in summary: guns weren't (initially) better than bows, but they beat out archery in that you can give any schmuck a musket and tell them to point it at the enemy and fire... whereas archery required a considerable time investment both at the level of production and of individual combat proficiency.