My favorite...? It's a hard question, because I feel there were pretty significant weaknesses to most of them. I think the characters were great, by and large, but I found most of the quests weak or awkward.
I suppose the one Iiked 'best' was Josephine's, because it illustrated a proof of character about her inclination towards diplomacy- that even when faced with personal danger and a pragmatic but deadly solution, she would work harder to a solution with less violence. The fact that the option to resort to Leliana's options was available, but she refused it, garnered respect. I can forgive the relative lack of content/action for that.
As for my trouble with the quests...
Cullen's story was well done as a metaphor for addiction, but as was raised earlier it ignored the point where the metaphor fails- lyrium gives Templars anti-magical abilities, which have real and substantial benefit. On an individual level I can understand and agree with his decision to break the habit, but I disliked how the whole 'anti-magic' angle of lyrium addiction was ignored or glossed over for the Templars a a whole.
Leliana is... well, I agree that she's a bit unstable. I don't think 'hardened' is a good descriptor of what she can be now, which honestly scares me. Even before reading the epilogues, I knew I wouldn't want her anywhere near power. I'll see how it comes across in an 'unhardened' route, but if a character arc is supposed to make you like a character more, it failed for me.
Josephine I mentioned. As a character-specific and illustrative story, it worked well for me.
For companions...
Cassandra's story arc I enjoyed as a testing of faith narrative. I just thought the quest about the Seekers fell flat. Lord Seeker Lucius was just crazy, even crazy-stupid, and the whole angle about tranquility cure was awkward. It was like I was supposed to be really moved, but... not. It didn't change the circumstances or the rational for the coverup in Asunder.
Varric's quest with Bianca was fine, but just not particularly exceptional. We were clearly supposed to find Bianca awesome and all, but to me she just came across as pretentious and a tone that felt like pandering to fans. It revealed the Bianca backstory for Varric... but I never particularly cared about that, or how it justified him being non-romanceable. I thought the Hawke arc was far, far better for his characterization.
Solas was... well, it was good about the lore of spirits and demons, and good about showing how Solas wasn't as reserved as he tried to be. But I thought it was a bit redundant about how his dialogue about spirits already covered most of his views on the subject. The murderous rage was revealing, but it made me feel he was really closer to spirits than actual people (a distinction we never quite bridged).
Vivienne was much too short and abrupt. There wasn't enough build-up or lead-in, certainly not enough to call it part of a character arc. More of a character flash in the pan?
Sera's was stilted towards sparking a fight, but not particularly on why it should be controversial. Maybe that was deliberate, and Sera particularly twitchy, but there was some mis-aimed arguments about responsibility being thrown around. I'll have to try the paraphrase at some point to see what they actually said, but it was hard to be nonplussed about it- after killing countless people who opposed you, somehow this one is a big deal?
Cole was great on terms of being revealing about the nature and possible evolution of spirits. Less so on why I should find it desirable. But I'll openly admit that I find Cole's actions akin to mind rape, and I don't find 'compassionate intent' or 'obsession' or 'it's for their own good' or 'he'll be a demon if you make him stop' proper justifications for it. I'll try the human route next, but I freely admit I am probably well outside the intended audience response.
Dorian's was... well, I thought it tried to hard, and on too political a subject. It felt too much like a metaphor for obvious real-world analogues, to the point that the in-lore applications or relevance felt eclipsed. Had it framed it more in terms of 'the dynasty must have an heir, and keep your desires on the side' rather than 'I'll mind-wipe the gay out of you,' it probably would have been my favorite story. As it was, it felt more like social advocacy slipping into my game.
And as for Blackwall... I think that in some respects his was the best character arc, even though I disliked him. Which doesn't mean I don't think he's a good character- I think he was very well done on multiple angles. I just happen to be closer to Cassandra's views of him- that he was masquerading as a good man, rather than properly seeking redemption for his own sins. I don't disagree that he's a good man seeking to repent, but in my views of justice and redemption you have to own up to your sins first. As far as I'm concerned, his redemption starts with his confession, not under his life as Blackwall.