In a YouTube video posted by PC Games (now set to private), Ubisoft Cinematic Designer confirmed that the PS4 version of Watch_Dogs will render at 1080p:
Of course there’s nuances to it. We are utilizing Xbox One to its full capabilities and the same with the PS4, of course. I know that, as far as to my knowledge, on the PS4 it will run in full HD.
The Xbox One’s resolution was not mentioned in the video, which is problematic considering the current rumors that it will run at 960p. However the Cinematic Designer did state that Watch_Dogs will offer the same experience regardless of platform choice.