The caracole worked right fine for the job it was designed for, namely dealing with pikemen and their inevitably accompanying musketeers through sheer volume of fire combined with the superior durability of armoured cavalrymen. It's not like cavalry could tackle pike by any other means than shooting them up anyway, not counting outflanking and suchlike.

It just wasn't a terribly effective tactic for dealing with other cavalrymen, not in the least because the pistols barely dented the sort of armour worn by heavy cavalry from beyond five meters; the reason it was nonetheless employed for the purpose for a while was primarily a question of the psychology and motivation of the soldiers who made up the heavy cavalry - mercenaries to a man and expensive to equip and train, both they and their commanders tended to be shall we say prudent on the battlefield.

Anyway, any decent war-bow in capable hands was by far superior a ranged weapon to any early man-portable firearm. Superior range and rate of fire for one. Firearms did have superior penetrating power to make up for their awful reloading times, much like heavy crossbows, but the very early ones in particular were pretty much short-range skirmish weapons. Crossbows kind of pwned them in effective range too.

What guns did have going for them (aside from issues like ease of use - they weren't much superior to the more accurate and longer-ranged crossbows in that regard either, AFAIK) was sheer psychological impact. The noise and smoke they made was just plain sacry, especially if they were fired en masse at close range - that they likely only caused superficial casualties was quite irrelevant in this respect. I've seen it claimed that in the first battle ever the Russians employed firearms against their ever-troublesome steppe-nomad neighbours, the latter were so disturbed by the first volley (which killed no men) they quit the field wholesale.

Terror weapons, basically. The more sophisticated arquebuses and muskets were actually some good also for killing people rather than just frightening them. In that, although they still lost out in accuracy, they did most of the things heavy crossbows could, some rather better, and also had a few subtler perks. One was the fact they could punch through things like ship railings and similar obstacles rather more effectively. Another was the relatively small size of their ammunition - a musketeer could carry as much as sixty shots' worth without particular difficulties, and this was regarded as sufficient for an entire battle. And they took up rather little space; that meant the musketeers could be more densely massed, compensating for lousy accuracy with sheer density of fire as well as the fright effect. And of course an arquebus make a whole lot better club in a pinch than a bow or a crossbow.

Respectable accuracy with even smoothbore muskets is perfectly achievable; after all, they were used by professional hunters too and those folks obviously weren't big on missing their mark. The thing just is that this takes a lot of practice, not in the least due to the habit of round balls shot out of smooth barrels tending to noticeably wander off their original trajectory rather noticeably, and this was something the rank-and-file musketeers of Western armies didn't get. Indeed, marksmanship practice was regarded as waste of costly gunpowder... Skilled shooters were nonetheless often picked out for marksman duties and often used by far more accurate rifled weapons; Gustavus II Adolphus of Sweden went so far as to raise a crack unit of marksmen from the gamekeepers of his royal hunting resorts when he went off to the Thirty Years' War.

As for the longbows, one gets a very strong impression they began to be increasingly relegated to what might be politely called "second-line positions" and decreasing in military importance and usefulness from something like mid-late 1400s onwards. I know they were still occasionally seen in the hands of English soldiery around the middle of the 17th century - poor mercenaries abroad who hadn't yet been able to get anything better and poorly equipped levy units mainly - but seem to have been considered indifferent for battlefield use. Personally I'm guessing this was simply due to ever-increasing proliferation of increasingly good armour. Well-padded mail alone can stop arrows launched from even composite bows (which are by far more powerful than self-bows like the English longbow), as well attested from the Crusades (and the fact the assorted composite-bow enthusiast cultures seemed to regard mail as perfectly viable battle gear). Even composite bows, nevermind now self-bows, need to be uncomfortably close by to have a decent chance of penetrating solid plate armour, an obviously challenging prospect on level battlefield but less of a problem for, say, Ottoman naval archers in boarding actions. By middle 1400s in any case just about any troops worth mentioning would be wearing at the very least mail topped with hardened leather or iron in some form or another; the well-equipped warriors would have high-quality tempered-steel articulated full plate. At least the front ranks of pikeman formations were regularly decked out in considerable amounts of solid plate already by the Late Middle Ages and by the 1500s at least a breastplate plus helmet was almost the norm. Thow in developements in field artillery and general improvements in overall military professionalism, discipline, organisation, battlefield command-and-control and tactics (ie. no more blind rushes à la Grecy and Agincourt), and one can see how the longbow found it increasingly difficult to make the cut.