> The Directors Cut is the unbutchered version.

The Director's Cut (released in 1992) drops the narration and adds the dream sequence, but despite the name is not entirely approved by Ridley Scott.

The Final Cut (released in 2007) is the only version where Ridley Scott had full final cut approval. It re-masters the audio, fixes some of the effects (replacing faces on stunt doubles, removing wires, etc), and changes a few lines (most notably "I want more life, father" instead of "fucker"). The color is also re-graded.

Some people prefer the Director's Cut over the Final Cut, especially the color grading, although I saw the Final Cut in 35mm when it was released and it looked pretty spectacular. In any event the changes in the Final Cut are nowhere near as egregious as the Star Wars special editions or the AI remasters of James Cameron's films.