In my "canon" playthrough, Alistair isn't a choice as he is King... so the choice is between Hawke and the Warden Stroud. Which makes it a very easy choice because I have no emotional connection to Stroud, haha!
In this playthrough though, I intended right from when I was doing my new Origins playthrough that Alistair would stay with the Wardens and be available at this point in Inquisition. I didn't really care about this particular Hawke and was happy to throw her away.
I don't think Hawke is dead though and is just assumed to be. There's a popular fan theory that I like:
And I like to think we'll see Hawke again in that case!
Interesting fan theory. It would be cool if this led to some unique DLC adventure of Hawke in this part of the fade.
I always forget that Alistair’s secretly royalty. Dragon Age Origins feels so long ago. I hope BioWare adds a lot to this series in upcoming years