From what I've seen so far, there's sadly not much characterization to be had in any of the side quests, which account for 75%+ of the game. You'll accept a quest like you would in an MMO and then turn it in, with really no chance to comment on the events of the quest or make a choice regarding its outcome.
The example that I can't stop thinking of, regarding how far side quests have fallen, was the small quest in Origins that you pick up in the Brecilian Forest called "Lost to the Curse" (Origins spoilers ahead, obviously).
The quest starts out simple enough: an elf named Athras tells you that his wife, Danyla, has been turned into a Werewolf. The leader of their Dalish clan says that Danyla is dead, but he will not permit Athras to see her body. Thus, Athras believes that Danyla is still alive somewhere in the forest and asks you to find her.
This is a pretty simple side quest, but during its course, it gives you quite a few interesting opportunities to characterize your Warden. When you finally catch up to Danyla, she tells you that she is in pain and asks you to kill her. You can:
1) Agree to kill her
2) Refuse to kill her, which causes her to attack you anyway, forcing you to kill her
You loot a scarf from her body. With this scarf, you can:
1) Return to scarf to Athras and tell him that she died of the Werewolf curse
2) Trade the scarf to a mad hermit in the forest. In this case, you can choose to tell Athras the truth of what happened to his wife
If this quest were to exist in Dragon Age: Inquisition, however, this is how it would play out:
You would walk up to Athras, who is marked by an exclamation mark on your mini map. You would talk to him and the standard non-cinematic dialog camera would appear. Athras would tell you his story in one or two lines of exposition, and then you would have two dialog options: 1) I'll look for your wife, and 2) Goodbye.
Once you have the quest, a diamond will appear on your zone map. You go to that location and find a Werewolf enemy in a clearing in the forest; maybe it's even named Danyla, though it's probably just named "Werewolf." The enemy is hostile so you cannot speak with her, and your only option is to kill her. After you do so, the quest updates and tells you to go back and speak with Athras. You go back and speak with Athras and you have two dialog options 1) I found your wife, and 2) Goodbye.
It's pretty disappointing, to be honest.
The main quests, which have actual cinematic dialog, offer the "standard" amount of characterization. I didn't feel like it was exceptional. It was just the usual amount.