When handguns had come into vogue, death rate of commanding officers increased tremendously. This corollary is probably the most vivid evidence of firearms superiority over bows and crossbows.
Proud commanders of the time were clad in finest armour of the age. They often emerged from battlefield with only minor wounds, being invincible to arrows, swords and almost anything else except for special anti-armour weapons like maces and spiked warhammers. How good that armour was in stopping bullets is a huge research topic but handguns definitely could pierce it more often than any arrow. Also, in 15th and early 16th century many prominent warlords fell victim to the fact that firearms could kill at the distance dimmed safe in the age of bows and crossbows.
But still there were miracles of surviving even bullet wounds.