Officially speaking, there's no Director's Cut of Prometheus coming to DVD or Blu-ray – yet – even though Ridley Scott has said that there is. He's also said, in more or less parallel interviews, that the film's many deleted scenes will be available only as stand alone items, selectable from the menu. It doesn't seem that he's quite sure yet what to do with the footage he didn't use.
Though I will bet you my house* that some kind of extended version shows up at some point.
In the meantime, have a gander at this little lot and get some idea what might be missing from the version we already have.
The following images, from the Facebook page of Creatures Inc., show you glimpses from an alternate version of the opening sequence. Perhaps these are from shots that simply got pruned away, or perhaps different iterations of some of the shots were filmed.
Two Elder Engineers, guiding their sacrificial ward. Creepy.
Several storyboards have turned up at Arrow in the Head, giving some ideas of how this scene was conceived before shooting.
Hardcore Ridley Scott buffs might be interested to see that we were going to end on a jaw. Scott had planned for the first scene in Blade Runner to end on a dislocated jaw too, evidence of freshly-killed Replicant, taken from the body to prove that the job had been done.
I guess he just likes jaws.
The first of these two new FX-showcase clips looks at the realisation of the scene we've been looking at above, but it its final, lone-Engineer version. The second looks at some of the sci-fi hardware. There's no doubt that a lot of good FX work was necessary to make Prometheus.
*I live in a flat, and it's rented.