For what matter bow and crossbow, it's more or less the age old debate of precision vs. saturation, the answer being eventually "it depends"
SATURATON OR PRECISION? DEBATE STILL GOING ON.
Duel between Genoese crossbowmen and Anglo-Welsh longbowmen at Crécy is only but an exemple of plurisecular debate opposing supporters of precision and saturation.
For the formers, optimal use is what matter : a minimum of projectiles for reaching the objective. For the seconds, only efficiency matters, and too bad for the expense in munitions.
Theorically, precision does have a good point : with precise weapons, a small number of shooters is enough to win, "waste" of munition is less important and fights are quick and decisive as every projectile have an immediate destructive effect. It's the advantage of crossbow, or battle rifle which was still used faithfully by many armies in the 60's instead of less precise assault rifles.
But the fact is theory is often wrong in face of tactical reality.
Apparently unefficient regarding ratio shot/reached target, saturation does have a superior psychological effect : if one elite sniper can indeed block a marching column, a rain of arrows or an artillery barrage can lead to dispersion, even panic.
Moreover, saturation isn't only for destroying but to fix the ennemy, in order to facilitate manoeuvre.
Actually, saturation and precision are often complementary : a naval battle, even with guided missiles, is based on the capacity to saturate defenses to strike the target...with precision.
The great force of Hundered Years' War bowmen was the ability to strike a precise target at 80m or saturate a zone at 300m.
And if the debate was actually a philosophical one? It's less the effective precision of strikes than the efficiency ideal that they represent that is seducing, against saturation seen as a waste.
Typical in military debates, where many disputes are more regarding ideologies than actual science.
BOW AND CROSSBOW : COMPLEMENTARY MORE THAN RIVALS
Battle of Crécy in 1346, where English bowmen crushed the Genoese crossbowmen on the service of French made bow's superiority a cliché.
But the question isn't that clear : both weapons have their adventage and defects. Crossbow are more precise : a mechanism stop the tensed rope and allow time to aim (on kneels protected by a shield named "pavois") when the bowman have to stand and shot as fast as he can to not break his bow.
Armed with a mechanism, the crossbow of XVth century don't need a great physical strength, and only some training days are needed to know how to handle it, against years for using a bow.
Moreover, the crossbow give more power at short range, allowing it (technically) to pierce every armor.
But the advantage is far less obvious regarding range : if crossbow reach can reach 400m, it's at the expense of precision and bowmen, by saturation, have as good results. With a superior "rate of fire" (12 arrows/minute against 2 bolts), bow are dominant in open field.
That said, medieval warfare is also about siege and naval warfare where crossbow keep advantage.
Direct tensed shot
Up to 80m, a longbow can shot directly. Usually, it means that a footman or a horseman is rushing at you and that you'll have to shot fast and get the hell out of here.
Half-Direct shot
Up to 200m, longbowman need to make a bell-curve shooting 15m above the target, 25°. It's mainly for shooting the rear part of the army, less protected.
Indirect shot
Up to 300m, 45° : here, the arrow gain penetration strength from the fall. Kiss precision goodbye.
Usually, it's first direct indirect shot, then direct tensed, then half-direct. But it's really context dependent
Once we mentioned bows and crossbows, tough, you still have the lot of other projectile weapons, but these tended to have less importance with time : the whole array of slings comes in mind, especially the
fustibal.
Javelins, or other throwed lances, were relatively common on the battlefield until the Xth/XIth centuries were they virtually disappeared, except in Spain. It was more widely used (especially due to the prevalence of skirmishes in medieval spanish warfare from one part, and the Arabo-Berber influence from another) both by the infantery (the anzcona, a short but heavy javelin) and by the cavalry known as
jinetes or
ginetes, which were eployed in Western Europe (during the HYW, for exemple).
I'm surprised nobody mentioned the mechanical, or counter-weight, artillery
It might have originated partially from the aformentioned fustibal, at least for what matter the
pierrière which was basically a gigantic sling manned by people (usually women and old people or children) as a defensive weapon during sieges.
But weapons as "couillards" ("they have balls"
for pretty obvious reasons), as they were based on mechanical and mathematical sophisticated principles, really appear after the Crusades and the arabic apport from Spain, Sicily and Palestine. It generally, if well manned, charges 80kg of projectile, up to 200m (maximum) with 10 shoots an hour.
And of course, you have the trebuchet, which was the king of sieges : its presence alone could force an ennemy to surrender. It was basically an augmented couillard, whatever for range (up to 2 000 meters for the best models, much less for the others), weight and size (altough, while stones of nearly one ton could be hurled by trebuchet, it was a relative exception). It was slow to charge after a shoot, but gained in precision so much that while gunpowder was introduced (at a time where it had little to no tactical effect save psychologically), trebuchet remained the basic device of a big siege. It was used up to Cortes' expedition, as at least one trébuchet was used in the siege of Tenochticlan.