Are you asking for picture comparisons of Alien or Aliens? Apologies of the confusion, it's just that Alien is the one that can be viewed as a new "Director's Cut" through seamless branching, and Aliens is the one that can be viewed as a "Special Edition" through seamless branching (it was always the Special Edition version on DVD before).

I have DVDs of both the Quadrilogy versions and older versions, so I could make screens for you. I've taken a look now, and I can tell you that the transfer for Alien is quite a bit sharper and has higher contrast than its previous version, but the transfer for Aliens is virtually identical to its previous version.

oojason: There is one negative difference between R1 and R2 of the Quadrilogy. The R1 commentary tracks run through both versions of each film, which gives more/alternate commentary for new seamlessly branched new scenes. The R2 only has commentary for the Theatrical Cuts of each film. So there's a bit less commentary.