I'm playing a Witch Doctor with exclusively fire-based skills. I chose to use The Burning Axe Of Sankis due to the large fire skill bonus. I can say this bonus is absolutely incredible and is pure bonus. By "pure bonus", I mean that a 20% bonus is a net 20% damages on every fire-based skill (I suppose every skill that is clearly noted as "fire damage").
My tests were performed as follows. First, I bought two axes with same dps (736.5 for the legendary fire-based axe and 737.2 for a random rare axe). Both axes didn't had any other dps modifier, except a 5% elemental damage on the legendary. I went on a map and compared the maximal crit I could get with both weapons (5-6 minutes with each). The difference was approximately the 17% of the legendary axe I bought (well, in fact the difference was more like 21%, I suppose this is due to the 5% elemental damage of the legendary).
Just a note : the fire-skill damage bonus is of course not reflected in my menu dps. It's some sort of "shadow dps".
Based on this, if you want to compare two weapons, one having an elemental-skill damage bonus, you should simply add this bonus to the dps of your char in menu when equipped with the weapon having the elemental-skill damage bonus (or dps computed on a web calculator if you are comparing some weapon in AH). This statement assume of course all of your skills are based on this element. It is almost true for my WD, it is certainly not true for a cold-sorcerer taking meteor.