As you may already know, Aura Espada's damages can be affected by Hide Attack, Shell Break, Spell Burst, Touch! (Special Support), Asura Aura percentage and perhaps more. (If you are aware of other ways to improve its damages, feel free to comment!) The base calculation seems to rely on Atk and Matk (and Crit damages in case of Hide Attack), and the autoskill is activated by defense, evasion and regular attack.
One more thing I thought worth mentioning is that a Shell Break Aura Espada occuring on High Defense beats my Monk's regular Shell Break by far... even if all of my Wyn autoskills do proc! (I wish these kind of defenses would last longer! >.<)
Here you can compare regular / Aura Espada Shell Breaking: