This choice made my head hurt the first time, and the second, and the third...you see a pattern here? In my first playthrough I had had Stroud as Alistair was king. At first I thought, bah, I'll leave the relatively unknown guy here and save Hawke, but after reconsidering I had other ideas develop. My Hawke is a mage, and the dialogue indicates that whomever you leave behind will "most likely die..." not definitely. So I thought this is a trick, they want me to leave Stroud because I won't leave my Hawke. Well out of the two Hawke is the only one in my opinion that would stand a chance against the demon. Hawke is also the first to volunteer to stay behind, stating that Stroud is needed to rebuild Wardens. Also stating that Corepheus is his (hawke's) responsibility. This last statement confused me at first. Obviously Cory isn't here, whats Hawke mean by that?
Anyway, I chose to leave Hawke that first time. I completed all the Warden table missions and all my wardens died to "poor choices" apparently lol. On second play through, I left Hawke again, and this time managed to complete all Warden table missions with minimal casualties and keeping high morale. On third play through I left Stroud, and was still able to complete all the warden missions favorably just as I had done on second run. So it seams those missions are not bound to your choice to leave/save Stroud. As far as I can tell only the epilogue is effected.
Varric's reaction to leaving Hawke was heartbreaking. It made me second guess my choice, and consider restarting that first time. However, after seeing the same scenes play out having left Stroud in Fade, it didn't have anywhere near the same impact and felt pretty weak. The heart wrenching outcome is more favorable to me if only for the fact it makes it more meaningful. Regardless Varric stuck with me and after that amazing game of wicked grace his taro card was no longer depressing to look at.
Now there's that bit about Cory being Hawke's responsibility. It occurred to me that at the end of last battle I don't just deal a killing blow to Cory, I make a point of saying "So ,you wanted into the fade?" or something like that, and then bam, I send him into the fade, albeit somewhat warped and possibly slightly crushed lol. So was Hawke in there waiting for him? Again, with my Hawke being a mage and having an understanding of the fade, and being bad ass enough in my opinion to beat the big spider (a note here: leaving Stroud he seams resigned to his death, leaving Hawke he makes makes a light hearted joke about "always has to be spiders"), maybe he knew something I didn't and wanted to make sure to kill Cory this time permanently. After all, if he was so insistent about it being his responsibility why didn't he come to final battle even when I left Stroud?
Then there's the possibilty of this being resolved in a dlc, totally guessing here, rescue mission? I still have anchor, why not go back into fade and get Hawke/Stroud out? Maybe different encounter based on who is left in fade, find Hawke and help him finish off big bad spider (not sure how time works in the fade, but Hawke is a survivor) or find Stroud beaten by spider and corrupted into new baddie and have to take him down? I don't know just possibilities/pipe dreams.
Now in my world state with Alistair as the warden, it makes choosing to leave Hawke behind a little easier. No way I'm leaving Alistair behind, period lol. After considering all this I just feel Like Hawke is the best choice to remain in fade, although not the easiest choice to make.