Damage starts off about the same. Wands cost 3 AP to attack (short range initially, increasing with 'Wand' level) and can also allow you to cast spells (with a limited number of charges), while staves are 4 AP (melee range) or 3 AP (long range, via Staff of magus, but with a 1 turn cooldown). Being one handed, wands benefit from the Dual Wield skill, to reduce the damage penalty and AP cost when dual wielding.
As demonstrated in some of the EE streams, you need to be more careful of surfaces you may be standing in or near when using wands. A staff is more of a backup attack after the beginning of the game, usually worth more for the bonuses than the damage.
