At the beginning of the 17th century, the overwhelming majority of infantry firearms around the world were matchlocks; China, Japan, the 'Gunpowder Empires' of the Islamic world, and European states were all using matchlocks in concert with more traditional weapons, like spears, swords, and halberds. By the end of the 17th century, with the War of the Grand Alliance and the War of Spanish Succession, you see in Europe armies uniformly equipped with flintlock muskets, with bayonets by and large supplanting the pike, while Asian states tend to keep using matchlocks and traditional weapons well into the 19th century. As I understand it, linear warfare was about massing firepower through infantry lines, and replacing pikes with bayonet-fitted muskets gave an army more firepower than if it was splitting its forces between melee and missile infantry.
Was the adoption of flintlocks part of this tactical divergence? Did they offer the infantryman significantly greater firepower, and were they better suited to bayonet use than their matchlock predecessors?
There are a number of advantages. GeneralLeeFrank mentions the quicker loading and firing and the position isn't given away, although that didn't matter as much in most battles and could be used as an advantage, as John Smith did against the Turks.
One of the biggest advantages is the relative safety of the flintlock over the matchlock.
I have fired both and keeping a musket and a lit match in one hand while you handle gunpowder with the other isn't the most ideal situation to be in. That is when you are concentrating on it. I can't imagine what it would be like in battle.
Neither weapon will fire well in damp conditions but it is possible to fire the flintlock in the rain once, even though it is less likely.
In addition to that you don't need to have them be as careful around the artillery train and all the gunpowder.
There is a big difference in the manufacturing of the two weapons though. The simple lever of the matchlock is easier to manufacture than the springs in the flintlock.
While I don't think the nature of the firearm's lock mechanism would effects its quality as a bayonet mount, the nature of the lock does have a major impact on the amount of fire a unit can give.
The first, of course, is that a matchlock requires a lit match (i.e. an open source of flame) around large groups of men all pouring and loading gunpowder. This tends to result in infantrymen standing further apart, so as to avoid any accidents. When you utilise a flintlock, you can stand your infantry closer together. The nature of the matchlock of course creates logistical problems. You must constantly keep the match lit, and thus continually supply more length of match to your troops. If the match is--for some reason--extinguished, your weapon becomes effectively useless. The need to keep the match lit to be ready to fire of course limits your ability to react when faced with surprise attack. Finally, rate of fire. As I understand it, a matchlock does have a lower rate of fire than a flintlock, mostly for reasons mentioned below. A flintlock can be ready to fire, whereas a matchlock will often have to check their match--replacing it into the holder, or ensuring it's properly lit--before they can give fire.
The combination of all these results in a situation where you can both thin out your lines--reducing them from 5 to perhaps 3--thus letting you bring more men directly into the act of firing, increasing your firepower. As you've noted, a big part of the wider trends during the early modern is the increasing reliance on fire, with pikes being reduced as a proportion of the army. A higher rate of fire with more of the men actually involved in firing provides a marked increase in the amount of fire one could put out.