We now take guns for granted and assume that they were always superior to bows or crossbows. Early guns were, frankly, pretty awful weapons. From Infantry Missile Weapons in the Renaissance:
By 1500 infantrymen had three different missile weapons available to them. There was the arquebus, a relatively light firearm manageable by one man, as well as the very common crossbow, and the longbow, which was mostly limited to use by the English. Technically the arquebus was inferior to both the other two weapons in range, accuracy, and rate of fire, while the longbow was generally superior to the crossbow.
Characteristics of Infantry Missile Weapons, c. 1500 Weapon Weight Proj Wt “MV” KE RPM Range (kg) (grms) (m/sec) (jls) (m) Arquebus 6.5 45 30 20 1 25 Crossbow 3.5 125 45 127 1-2 50 Longbow 3.0 75 45 76 2-6 50 Relatively speaking the arquebus was cheaper than either the longbow, which had to be meticulously handcrafted from yew, and the crossbow, which required equally meticulous workmanship and rather expensive steel as well. The arquebus could be mass-produced by a foundry in fairly cheap cast iron. In addition, while the range, accuracy, and effectiveness of an arquebus round were inferior to those of the other weapons, an arquebusier could carry more ammunition than either of his competitors. Arquebus ammo weighed less than arrows or crossbow bolts, even after adding in the powder charge.
Rounds in Three Kilograms of Ammunition Weapon Round Arquebus 50 Crossbow 24 Longbow 40 As a result of this difference in ammunition weight, an arquebusier could sustain fire longer than either a crossbowman or a longbowman. And ultimately it was sustained fire that won battles, more than accurate fire.
In addition, despite the inferior technical performance of the arquebus ball, it was superior to arrows as an armor smasher. Rounded, soft lead bullets were less likely to be deflected by the polished curved surface of armor than were arrows.
The arquebus had one more very important advantage over its rivals. It was perhaps the critical advantage in determining the rather rapid conversion of armies from archers to arquebusiers. A man required considerably less skill to become an arquebusier than either a crossbowman or a longbowman. A few weeks training was all that was necessary to turn out a fairly capable arquebusier. In contrast, it took years to properly train a the bowman, who had to develop considerable musculature before being able to use his weapon to its fullest capacity. This was particularly true of longbowmen, of whom there was a saying that in order to a good one you had to start with his grandfather.
One other advantage of the arquebus is that it’s much, much more frightening than a crossbow or longbow.
Edit: It didn’t hit me at first, but the muzzle velocity the article lists for an arquebus, 30 m/s, is about 60 mph. I suspect I could throw a bullet that fast. From what I’ve read, an arquebus has a muzzle velocity closer to 1000 fps (like a modern pistol), or 300 m/s. Fixing that typo reveals that an arquebus round has a kinetic energy of over 2000 joules, not 20.