Interesting discussion. i have a few points, forgive me if some of these were already covered.
Firearms
Guns were very
hard to use at least initially, and required skilled labor (well trained troops) until a series of inventions in the 15th Century made them easy to use for infantry:
Corned and filtered powder
The slow match
The match-lock
The arquebus 'shape' in it's various variations.
Firearms didn't become widely adopted for cavalry (or mounted infantry / dragoons) until the advent of the wheel lock.
In the late medieval period, the time when firearms and crossbows and bows were most often used together, firearms were mostly used by highly skilled troops, elite among the Swiss, German, Flemish, and Italian urban militias, and Bohemian (Czech) Hussite heretics, both on their own land and fighting as mercenaries. Bohemians and German urban militia made up the bulk of the Fekete Sereg or 'Hungarian Black Army' which was arguably the most effective late medieval army, certainly the most heavily invested in firearms.
During the late medieval period, gunners were protected by pavises, mantlets and war-wagons. This was pioneered by the Czechs who were the first to make widespread use of firearms in the open field. Medieval firearms were typically also mixed with light cannon and volley guns etc. Before the Hussite Crusades firearms were mostly for siege warfare. In the west firearms seem to have shifted to protection by pike squares in the 16th Century. It's not clear to me why, but maybe it's due to the increasing ubiquity of medium caliber cannon.
In the 14th through 16th Centuries, training for guns and for crossbows was mostly done by elite shooting societies and put to the test in these rather expensive formal shooting contests, mostly organized by Free Cities and City States. Still a remnant of the tradition in Switzerland and Italy. The Germans called these 'Schutzenfest'
https://en.wikipedia.org/wiki/Sch%C3%BCtzenfest#History
If you dive into the records of the Schutzenfest and Italian equivalents you can learn a lot about
actual capability like ranges, accuracy etc. in the periods roughly 1350-1550 for both guns and crossbows. i think there is also the equivalent type of records from England for longbows, they had all kinds of archery contests both for individual targets and clout shooting.
It's worth noting, that rifling was not invented in the 19th Century but existed in the early 15th - rifled firearms were considered cheating in those shooting contests and records show they were sometimes confiscated (but subsequently kept in arsenals by the towns). Same for several other inventions we associate with the modern period or the 19th Century like rifling, revolvers, breach-loading firearms, and many rather other startling innovations, which you can see in the 15th and 16th Century.
I mention this because it speaks to the mystery of why certain weapons and systems were abandoned in the Early Modern period. I think the reason were more social, political and economic than technical but I admit that is just a theory, i don't really know.
Bows
Effective range for well trained archers seemed to be much farther than 200 meters. Look at the records of the medieval warbow society. It sounds like the effective range for 'clout shooting' is more like 300 meters. Archers always had both 'direct' and 'area shooting' modes, the Mongols and Ottomans did that too, as did the Mughals. Not sure about the Manchu etc. but I assume it's the same.
http://www.theenglishwarbowsociety.com/
I'm sure it varies greatly by the exact time and place but I do not think they had low quality arrows. Craftsmanship particularly for weapon was at a generally very high level, controlled by the guilds, at least in Central Europe and Italy. I don't know about England but I'd be very surprised if they had substandard quality arrows.
Bows seemed to retain a niche in naval combat for a while after they had declined in use on land. The Mary Rose comes to mind of course, but archery was still a major component of war in the Med in that same era. Some military historians speculate that the loss of skilled archers at Lepanto is a major reason for the subsequent decline in Ottoman naval power.
Crossbows
Crossbows seem to have gotten very effective, even for mounted troops, by the late medieval period, but they were expensive to make, as were the spanning devices, and training was expensive too. I suspect their decline had again, more to do with social changes than for technical reasons.
Armor also comes into play in all this of course, but that is almost a new dimension of complexity. I think both armor and expensive weapons like the higher end crossbows declined with the shift toward more 'unskilled labor' for the bulk of armies very generally speaking in the period roughly 1550-1650.
J