There are quite a few aspects of Dragon Age 2 that I preferred over Dragon Age: Origins. First and foremost, I really enjoyed the voiced protagonist. While I can certainly enjoy games with silent protagonists, Bioware games focus heavily on dialogue, and at least for me, it's important for my character to be an active participant in the dialogue (both vocally and visually, through facial, hand, and body expressions).
Secondly, I enjoyed Bioware's shift away from the approval/disapproval system. While the friendship/rivalry system isn't perfect, I liked how it allowed players to disagree with companions and still feel as if the relationship progressed, as well as the ability to challenge parts of each companion's worldviews (in DA:O, it was restricted to Alistair and Leliana). While I'm not expecting Bioware to keep the friendship/rivalry system intact for the next game, I hope that they continue to move forward in that direction, rather than go back to the approval/disapproval system.
In regards to combat, I really liked how it was more responsive than the first game. I very much disliked how melee characters in DA:O had to slowly walk up to a target before attacking. In contrast, I enjoyed how warriors and rogues in DA 2 quickly closed distance between them and their targets by either lunging or leaping.
While I can certainly think of more elements that I enjoyed from DA 2, I'll simply limit it to these aspects for now.