A film centered on the search for Osama bin Laden, much as the controversial Zero Dark Thirty is, Manhunt leverages interviews with CIA veterans, including analysts and a former chief of counterterrorism. There is also archival footage included of interviews with bin Laden, which gives the viewer greater insight into the backstory of how the head of al Qaeda rose to such prominence.
Having seen both films, the nonfiction account in Manhunt is somewhat more interesting just because of the people interviewed "“ particularly the women who worked as analysts at the CIA on whom the character in Zero Dark Thirty is based. To see their reactions to the retelling of what's probably the greatest thing that we, the American public, will ever know about is somewhat fascinating.
While the dramatized version of Zero Dark Thirty has the benefit of using explosions and car chases to keep people interested, Manhunt is heavily reliant on some fairly dramatic lighting, fantastic editing, and impressive visuals. I don't think the documentary will suffer from being released so close to its dramatized counterpart; it will probably benefit. I know I was curious to see how closely the stories related to one another.