Watch Dogs will run in "full HD" (1080p) according to the game's creative director, Lars Bonde. Bonde said the following statement in a Youtube video posted by PC Games (since made private):
"Of course there's nuances to it. We are utilising 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."
Because the video was taken out of the public eye, it is possible that Bonde's claim of the PS4 running at 1080p was inaccurate or was not meant to be announced at this time. The Xbox One's resolution is still unconfirmed, but rumors are currently swirling around that it will be at or about 960p.