They work together?Which one is better?
Yes. Double strike affects it. Also one is not better than the other per say. Extra attack is for skills that benefit from it. Primarily primary skills (get it), or special skills with the Discordance Mythic. Fits the similar niche or reign as Multi Attack affix.
Double strike affects any damage though, with a chance to deal it again. Specialist is like this but repeating a skill instead of any type of damage. Can double strike a crit, deadly strike, elemental crit, or anything else.
So yes you can combine both but its optional. You don’t have to.