Smite

Smite is the anti-undead melee enchantment: it adds nothing at all to a normal hit and a great deal to one landed on an undead mob. That covers zombies, husks, drowned, zombie villagers, zombified piglins, zoglins, skeletons, strays, bogged, wither skeletons, phantoms, skeleton and zombie horses, and the Wither itself.

Each level adds 2.5 extra damage against those targets, so an enchanted sword hits an undead mob far harder than a Sharpness sword of the same material — and hits everything else for exactly what an unenchanted one would. Against creepers, spiders, endermen, the Ender Dragon or another player it is dead weight, which is the whole of the Smite versus Sharpness argument.

The two can never share a weapon: Smite, Sharpness, Bane of Arthropods, Density and Breach all lock each other out, so the choice is really about which weapon you are committing. Sharpness belongs on the sword that has to handle whatever appears; Smite belongs on a second weapon kept for undead work — a Wither fight, a mob-farm grinder, or the skeleton-heavy floors of a dungeon or ancient city. On a mace the question disappears, since a mace cannot take Sharpness at all — there Smite competes only with Density and Breach.

It applies to melee weapons only — a sword, an axe or a mace — and does nothing on a bow, a crossbow or a trident. Beyond an enchanting table it comes from librarian trades, from fishing and out of chest loot as an enchanted book, and combining two equal-level books on an anvil produces the next level up, usually a cheaper route to the top tier than gambling at a table.