Similar to Call of Duty: Ghosts, in order to play Assassin's Creed 4: Black Flag in true native 1080p on PlayStation 4, you'll need to first download a title update. Ubisoft explained this is because the version of the game that shipped is being rendered on next-gen at 900p and goes through a upscaling process.
Ubisoft believes "some players might not even be able to tell the difference," as the upscaling barely adjusts the image. If you can spot the differences you might just notice that the game, "in some very subtle ways," will be slightly less crisp but a "tiny bit smoother."
“If it’s running at 720p vs 1080p, you’re going to notice the difference, by far,” Associate Producer Sylvain Trottier explained. “But if it’s set at a resolution that’s very close, where most of the pixels are already there in internal processing, most people won’t see any difference.”
Ubisoft justified shipping the game at 900p in order to meet an essential goal: "deliver a visually brilliant game at a steady 30 frames per second (the industry gold standard for open-world games).
"Finishing the game at 900p gave the development team the extra room in terms of the GPU and CPU usage to ensure the framerate never dips below 30 frames per second," Ubisoft continued. "The team then used the time between the ship date and the release to focus on a title update that could deliver native 1080p resolution on the PS4."
“The most important part of this title update is not necessarily 1080p native resolution,” Trottier added. “It’s the fact that even when we were done with the project, even when we were finished with the certification and everything else, even when most of the engineers had started to work on other projects – like we always do at Ubisoft – some of my engineers continued to work on Black Flag and they even developed a brand-new anti-aliasing technique.”
It's worth noting that Call of Duty: Ghosts' day-one update (about 700mb) did not take much time to download, and I have terrible internet speed at home.