The sight of John Hurt as a Doctor is something else, something that makes a fan yearn for the possibilities of what never happened in the past...imagine a true John Hurt-portrayed Doctor during the classic years...maybe it would have extended the series past 1989...
Anyway, the War Doctor as a character is equally something else. Although he officially appears in three episodes, the War Doctor probably has a lot more offscreen history due to being the one who was in the Time War, and the distinction of being the one who destroyed the Daleks and took his home planet of Gallifrey with them. Because of the brevity of the character's onscreen appearances, it's difficult to form a fully developed opinion, beyond gushing over how John Hurt played this character with a combination of the First Doctor's wise gravitas, the Second Doctor's dark side, the Third Doctor's magnetic presence, and the Eighth Doctor's youthful buoyancy (particularly in the scenes with Billie Piper and Jenna Louise-Coleman).
As a concept himself, the War Doctor occupies a uniquely divided area. Moffatt correctly predicted Eccleston not returning to the part of the Ninth Doctor for the "Day of the Doctor", but I think he was especially wrong in presuming that the Eighth Doctor wouldn't be the one who ended the Time War. Considering the direction the character was taking and has been taking in the audios, there's some credible debate as to whether or not he could have been the incarnation of the Doctor to end the war. There's no doubting that he has considerable hatred for the Daleks...but could this incarnation of the Doctor been ruthless enough to destroy his own planet? It's a question that we probably may never know, unless either Big Finish gains the full rights to the new series and can do some explorations of the Time War or during Season 8 of the new series we see some references to the war and its impact with the impending return of Gallifrey.
Ideally I loved the idea of the War Doctor...the character rejecting the name "Doctor" is almost a return to the dark, angry period early in Pertwee's run. I'd love for Hurt to do some audio plays relating to this incarnations adventures during the war, maybe not feature actual battles during the war itself but who is to say that this incarnation didn't return to doing covert operations for the Time Lords, maybe even working with the Derek Jacobi version of the Master during some of the missions. He'd probably reject the idea of taking on companions, just because of the wealth of danger apparent, but I can see him taking on "assistants" for one time status. Just because he was the dark incarnation didn't mean he rejected his principles of helping others where he could.
It's like Matt Smith said...he was the Doctor on the day it was impossible to get it right.