The core difference
The bow draws and fires in one fluid motion — hold, aim, release, repeat — with Power V dealing the biggest single-shot damage. The crossbow loads in advance and fires instantly on trigger: slower sustained fire, but the loaded-shot ambush hits the instant combat starts. A crossbow can also hold multiple loaded arrows with Multishot-era mechanics and fires firework rockets for AoE damage.
Enchantment splits
Bow: Power V, Infinity (one arrow forever) or Mending (pick one — Infinity and Mending are mutually exclusive), Flame, Punch. Crossbow: Quick Charge III (faster reload), Multishot (three arrows in a spread), Piercing IV (arrows through mobs and shields — the PvP anti-shield answer).
Which to carry
Most players carry a bow as the primary ranged weapon and keep a crossbow pre-loaded as the "first hit" opener — swap to the crossbow, fire the ambush shot, swap back to the bow for sustained fire. Crossbows also work while holding a shield in the offhand... with the trade-off of slower reload cycling.