Shadowheart, and it's not even close. I got emotionally invested into that character in a way that no other video game has matched.
Her build-up in act 1&2 is good. I do enjoy a bit of mystery in a character. It all led to an excellent climax in the shadowfell, this my favorite moment in the game. But the way her quest ended in the house of grief was something else. Coming back there to face a lifetime of abuse and manipulation, coming out victorious only to have her parents die anyway. I was already sad after that. But when the little long rest scene started playing where she was crying, it just absolutely gutted me. I put the game down for a week and went to touch some grass. It also inspired me to pick up my old guitar and learn to play some of the soundtrack (I can play the nightsong now :-D). I know she has a dark justiciar path as well, but I doubt I can ever bring myself to explore it. A cult trying to mindwipe and break you, and then failing because of sheer strength of character is both tragic and inspiriting at the same time. One of her lines near the end of act3 captures it perfectly. "It would have been so much easier just to turn into a monster". Yes, yes it would have been.
So, her story moved me and got me off my lazy ass to play guitar again. That has set a high bar.
I like both Lae'zel and Gale. Lae'zel has a strong-willed, no-nonsense practical attitude that you just must admire. While gale has some of the most articulate dialogue in the game, which I quite enjoy listening to.
Karlach and Wyll are fine. Although I must suspend my disbelief with Karlach significantly. I have a hard time understanding how someone with her backstory could act so cheery and naďve. As for Wyll, I would care for his story a lot more if he wasn't so damn arrogant.
That leaves only Astarion, which is the only origin character I cannot stand. I never gave him a chance to be fair, because I can't look past his cringe, edgy boy attitude. Whenever he speaks, I want to ram a stake through his ribs.
I'm not going to comment on the non-origin companions since I haven't explored them enough for my liking.
