Okay, well, less enthusiastically, I just think he was a better mage. Anders would have to give himself over to the Demon, and then it's not really Anders versus Dorian anymore. And Dorian's fought dragons and giants... what did Anders fight? A grumpy cat? Hurt feelings?
Dorian would win without even messing up his hair.
Haha, less enthusiastically, oh, yes, and not biased... Okay: What Anders fought against? Darkspawn. Templars. Broodmother. The Architect. Corypheus. Dragons. Demons. Abominations. a Forbidden One. Epidemics. And he (almost) defeated Dog in Wicked Grace... (The two grumpy cats were his helpers, not his enemies.)
Awakening Anders vs Dorian: both can win, Anders not so underdog, what you wrote: a spirit healer is strong, focused mage. And still: he's not only a healer. Anders/Justice vs Dorian: Anders win. No doubt.
True, Anders lost his ear ring... (Side note: Justice's not a demon. He prefers SPIRIT!)