The passive Poison Damage skill does not require potions, but only adds to melee attacks and (depending on the level) has up to a 30% chance of being triggered each hit. The Poison Weapon skill is separate, is triggered every hit (up to a limit based on the skill level) and can be applied to bows (which IIRC is more effective then Poison Arrow), but requires potions.
If you are playing a melee warrior, Poison Damage is easier to use. I didn't try it, but Stun has a similar chance to hit (a little lower), and I found that quite helpful once maxed. The amount of damage from Poison Weapon could be greater (it depends on the poison used, but I didn't search for any specific values), and would probably be more appropriate if you wanted to actually roleplay the character type.
The Locus Inn - Skill System (individual paths, and a skill table for each class)