Diablo – What are the primary stats for each Champion

Class specific weapons can provide some class only enchantments that you cannot get on standard weapons. Whether or not this is worth a trade off for damage, that is entirely up to you to decide.

For instance, you can find a demon hunter only 1 handed crossbow that provides hatred regeneration or a wand for mages that provides improved arcane pool.

Like James mentioned in his answer, the demon hunter is the only class that has a unique situation where you MUST have a ranged weapon equipped or you can't use his ranged attack skills. And his one handed crossbow is the only ranged weapon you can dual wield.

The only difference between the gendered classes are aesthetics, both in visual appearence, and in audio voiceovers / text. (Mostly pronouns)

The individual stories for the classes (the parchment-style cutscenes that play on the completion of most major quests) also vary between the genders.

Perhaps the biggest differences are in the dialog between the player character and their follower when playing solo. When interviewed about it, one of the Blizzard devs said that he particularly enjoyed the dynamic between the Scoundrel and the female Wizard.