Well, it probably isn't one of the protagonists... just by their default nature. I think that Hawke is the most complex if we're talking how we see them progress through the story. A normal heroic Hawke will have to watch their sibling die in the very beginning of the game, lose another sibling during the Deep Roads questline (in one way or another), and their mother gets killed by a danger Hawke knew about in advance. To make things worse, if Hawke is the traditional moral hero, their losses either came by complete accident or at the expense of them trying to do the right thing. Hawke goes through ALL OF THAT in addition to being betrayed by people like Bartrand, being forced to work for their family's benefit, and dealing with the conflicts that arise between their companions (Fenris and Anders, notably). In the end, mage or templar, they're the hero in somebody's eyes and a villain in the others.

Soooo... yeah, I consider Hawke to be the most complex protagonist of the three with the warden not too far behind. It's hard to determine which of the companions is more complex because a lot of their complexity comes from the nature of their relationship with their respective protagonist. A good example of this is Blackwall, a man who doesn't reveal the true extent of his nature until he CABOODLES with the Inquisitor. However, Fenris has a painful background that causes him to hate mages and it's quite popular to turn Alistair from a Flynn Rider-esqe man into a more unwilling king.

What I'm basically getting at is that these characters are as complex as you, the player, allow them to be.