MOVIE-CENSORSHIP.COM has only a comparison between the ALIEN theatrical version and the director’s cut.
I don’t have a Blu-ray drive, so cannot provide any screen shots.
Anybody still owning the old QUADRILOGY DVD box set - or the 2003 2-disc DVD release of ALIEN - as well as the current ANTHOLOGY Blu-ray release, (or just the Blu-ray release of ALIEN) can check for themselves.
I’ve the Anthology Blu-ray disc release. 1999 DVD release too. Kind of counts but I have no idea why it should.
Movie-Censorship.com has tons of version comparisons so there’s that.
The 1999 DVD release of ALIEN was only the theatrical cut. To view the differences between the 2003 & 2010 DIRECTOR’S CUTS, you need the 2003 DVD release of ALIEN (which included both the theatrical and the then new director’s cut) and the 2010 ALIEN Blu-ray (which also includes both cuts).
An example: The bonus creature shot of the Alien dangling near the chains above Brett before it attacks. This shot is exclusive to both director’s cuts. Compare that shot between the 2003 & 2010 director’s cuts and you will see they are different takes of the same scene. The camera pans up and almost past the Alien (for the 2003 version), and for the 2010 version the camera is still and stays on the Alien
I checked your link and there is only a comparison between the ALIEN theatrical and director’s cut but no comparison between the two versions of the director’s cut (2003 & 2010).