The main appeal of The Last of Us Remastered is its graphics upgrade over the original PS3, even though there are other bells and whistles added to the remake.
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How great of an improvement are the new visuals? IGN has put together a video comparing the two side by side, which is the most effective way to view the differences. The video is embedded below for you to judge on your own, but it's pretty clear the PS4 version is much-improved.
Part of the experience is the higher framerate, which you'd likely only notice while playing (or, at least, it would become more apparent). While the positive effects of this during cutscenes is up for debate, it should make the gameplay segments smoother.
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The more obvious change comes from the improved resolution, now 1080p compared to the PS3's 720p. Character models are much clearer, and environments more defined (check out the bricks behind Joel in early in the video, and his clothing).
There are those who simply don't pay attention to--or care about--resolution differences in games, and to each his own, but the improvements are definitely there in The Last of Us Remastered.
In addition to the improvements in visual fidelity, the remake includes PS4-specific features such as the use of the controller speaker to play audio logs. The light bar will flash and change colors to reflect damage, and you can swipe the touchpad to open your inventory. The game includes the additional multiplayer content released since the launch of the original game, as well as the Left Behind DLC.