To the OP, make sure you research this because I feel your pain. There is a difference in the DP skills AND the skill tree (chains). I am still trying to find a site for Elyos VS asmodian skill chain. Unfortuatenly, from what I have seen in game so far, Asmodians have cooler chains than the Elyos. Quick Examples:
You see the part where he changes to Shield + sword the first combo? It's a three part combo... elyos don't have the third part of that combo... I am sure there are more difference depending on class, but mostly, Asmodians has more chains than Elyos. Also Elyos DP attacks heals for a puny amount where Asmodians does more dmg... I.E: Assasins...
Another example take a look at this two and you be the judge of which you wanna stand beside in battle:
VS
Which will you rather stand next to?