Director's cut includes the DLC The Missing Link, improved graphics and gameplay, commentary from the Edios Montreal on the level designs, gameplay styles, additional achievements.

And it's good to play Human Revolution, that way you will know about the story before Mankind Divided. And yes, the new game have a 12 minute video recap of the first game, but it is better to experience the whole first game through. (The recap is like the interactive storyboard for Mass Effect 2 and 3, but minus the decision making)