Crossbows = higher Damage?
If you like numbers

Lets do the math (a moderate charater + equipment, no special ammunition and enchantments on bow/crossbow)
100 Skill + 5/5 Perk + Legendary smithing + a 40% archery boost from equipment
Best Crossbow + ammunition (enhanced dwarven + dwarven bolt)
(22 + 10) * (1 + 0,5 * 100 / 100) * (1 + 1) * (1 + 0,4) + 14 bolt
= 148 (+ 50% ignore armor)
Best Bow + ammunition (dragon + dragon arrow)
(20 + 10) * (1 + 0,5 * 100 / 100) * (1 + 1) * (1 + 0,4) + 25 arrow
= 151
conclusion:
unarmored target = bow
armored target : crossbow