For the most part the Assembly Cut only removed scenes that contradicted new ones, or replaced scenes entirely. There was only one example I could find of a scene being taken out of the Theatrical Cut otherwise.

There scene just before the final battle begins, where we see prisoners David and Jude going over the plan one more time just to make sure they understand what to do. The scene ends with Jude leaving and David muttering to himself "This was her idea". I like this scene as I feel it adds to the confusion and fear of the prisoners.

We then cut to a short scene showing Aaron wiping a mirror clear and looking at his reflection. This recreates the scene earlier where Ripley has just shaved her head and wipes the mirror to reveal her new look to the audience. I like this shot, as I think in some small way it shows the conflict brewing within Aaron.

Both of these small scenes were removed in the Assembly cut, so I've put them back in.

Ripley's final scene in the film, where she makes the ultimate sacrifice, is a great send off for the character and a fitting end for the trilogy. As she states earlier, the Xenomorph has been haunting her for so long she can't remember anything else. This sequence, in both versions of the movie, had issues I wanted to fix, so the Legacy Cut ending is a mixture of both, with some new tweaks.

The scene initially plays out as it does in the Assembly Cut, with Bishop's extended sales pitch to Ripley, his demand of "no pictures!", and his pleading with her that he's not a droid. One of the problems I had with the Assembly Cut ending is that the score has been rehashed to match the new sequence of events, and it just doesn't work. The score is one of the standout features of Alien ³, and here it just feels butchered, so from the moment Morse locks the breaks in place and the platform stops moving, we've now moved back to the Theatrical Cut.

I've included a shot of Ripley staring down Bishop, as I really like this close up before the fall, but I've taken out the "you're crazy" line as it just didn't work for me. The slow lean in to Bishop has been trimmed down to just come in when he's asking "What are you doing?", as the first part of this shot has been repurposed.

Ripley falls backward, and we stick with the Theatrical Cut, as I just prefer the Alien coming out. The argument that her sacrifice meant nothing because she couldn't have survived anyway never landed with me. She wouldn't have survived anyway as Weyland Yutani would have chopped her up and discarded her, or worse kept her alive to study. The sacrifice is no less meaningful because she didn't know when the Alien was coming. She didn't tell Bishop no because the birth was imminent, she did it because she thought he was lying and wouldn't take the risk.

Not to mention, it's just more cinematic. Now that the chest-burster scene has been cleaned up, recolored, the flickering removed, and the birthing animation reworked, it's a great shot. Her just falling into the fire was always anticlimactic in my opinion.

Ripley actually falling into the flames is a nice shot (in theory), but in both cuts it lingers too long. I've reworked the sequence so that just before she disappears into the fire, we now see a reaction shot from Bishop (The repurposed shot from earlier), and another of his crew. The timing was worked perfectly so Ripley lands just as the score peaks. It lingers only a moment and now cuts to the furnace being shut off.

This sequence was one of the most difficult to edit, but I'm very happy with it. I hope it improves your viewing experience of Alien ³.

This is a small edit of a minor issue, but one that always irked me.

It's obvious from the red blood instead of white, that the character trying to convince Ripley, is indeed a human and not a droid, so why he's listed as 'Bishop II' in the credits seemed like a continuity error.

It's widely known in the fan community, and even referenced in extended lore, that he's not only human, but ranks quite highly in the Weyland Yutani organization. As such I've altered the end credits of the film to call the character by his actual name, Michael Bishop.