But DA:O doesn't just have combat solutions. It has a bunch of combat, and then it ends with everything going the protagonists way because you killed enough people. The only difference between DA2 and DA:O is that Hawke can't pick the persuade option to calm Meredith down when Anders goes all nuclear on everyone.
I dunno, you can CHOOSE not to kill the mages in the tower, choose not to kill Eamon's son, choose not to kill the werewolves, choose not to kill Flemeth, choose not to kill Loghain, choose to get the Landsmeet on your side so you have to kill fewer of them. You have quite a few choices that involve NOT killing people. It's true though, that no matter what choices you make, you always kill the Archdemon at the end. The Warden will always succeed.
By the same token, Hawke will always fail to stop the mage-templar war. Both are required parts of the story that is being told. Ultimately the question is of which story you prefer- the story of someone striving but falling short, or the story of someone ultimately succeeding.
Now within the context of those narratives, the characters are quite comparable. It's certainly true that Hawke was in many ways just as good at killing people as the Warden, I've always liked to imagine that the difference between the two was focus. Hawke had an introverted focus. The world was comprised of Hawke and Hawkes family. Later Hawke's friends and close companions become a kind of surrogate family, but the focus doesn't change. Hawke didn't really care about the well-being of the city of Kirkwall, preferring to hang out with his/her friends at the Hanged Man rather than play politics and shape the course of things. Ultimately this willingness to go where the road takes him/her is what causes Hawke to be unable to succeed. The solutions to Hawke's problems often aren't violence, rather the violence is created as a symptom of the problems Hawke encounters.
The big difference between the Warden and Hawke is that for the Warden, violence IS the answer, and in fact, the ONLY answer to the Warden's major problem, the Archdemon. The Warden also takes a hand in involving themselves with the people who set the world on its course. The Warden's problems can be solved with violence many times because the Warden maneuvers it to be so. Thus the Warden's focus, more extroverted and concentrated on the world at large, allows some control of his/her own destiny.
I find them both intriguing characters, but I like the Warden better because I feel like Hawke never lived up to the potential he or she showed. The game was advertised as the story of a rise to power, but ultimately it wasn't really. Hawke never really seems to want political power, otherwise he/she would have done more in the third act towards obtaining that goal. Instead, he or she is content to choose either the mage or templar side, rather than seek to take the reigns and seize power his or herself.