Physical damage (and Magical damage on mage weapons) is used to determine the general effectiveness of skills. Typically, a weapon with a higher damage rating just means you will be more effective overall. You are correct about DPS.

Faster weapons tend to have lower AA ratings, where slower ones have a higher rating. The damage you do with skills takes your AA damage into account (so for example, a 150 potency skill will do 150% of your AA damage) so a weapon with higher AA damage, with the same base Damage, will do more damage with skills. However this is overshadowed by the Damage rating of a weapon, which is the single most important stat in picking weapons.

Someone might be able to correct me if any of this is wrong.

Also, just to throw it out there because new players don't seem to initially realize it, but Magic Damage also boosts the effectiveness of healing spells.