In the original ending, the cult of Thorn kidnaps Kara and Danny Strode, intending to curse Danny with the sign of Thorn just like Michael Myers was as a child and make him kill his mother in a blood sacrifice. Kara is tied to a sacrificial altar in the bowels of Smith's Grove Sanitarium. They're saved by Tommy, who eventually stops Michael's pursuit of them with the carved stones he calls "the runes of light," which he explained to Kara in an earlier, also deleted scene as being the bane of the sign of Thorn. These rune stones are arranged in the Shape's path by Tommy, and when he steps within their circle, the Shape is frozen in place, like a mystical ward. Tommy then escapes with Danny and Kara, leaving Dr. Loomis to return, and face Michael and Dr. Wynn in the final scene.

In the full-screen version, you can see that Mrs. Blankenship has a Thorn rune tattoo on her wrist when she holds up the knife. This isn't visible in any wide-screen versions.

There is a version of this sixth Halloween film which has many scenes not shown in the theatrical release, as well as a different title/logo, different character developments, and a different ending. This "Producer's Cut"'s most noticeable differences are:

The movie begins with a flashback to 1989 in which Jamie is kidnapped by the Man in Black before the police station explodes.

Dr. Loomis (Donald Pleasance) does the voice-over narration at the beginning of the movie, not Tommy Doyle (Paul Michael Rudd).

Michael Myers does not kill Jaimie Lloyd right away; she lingers in a hospital for half the movie, and is eventually shot by the Man In Black.

There is a very different ending to the movie which replaces everything after the scene in which Kara is captured by the cult members.

In the home video version, when the father is killed by Michael Myers in the basement, the massive dose of electricity his body takes causes his head to explode. In the alternate cut, for some reason, this is not shown.

According to the official Halloween website under the FAQ section, some scenes from the producers cut are shown in the television cut for the UPN network.

The "strobe light/operating room" scene (only seen in the Theatrical version) was originally going to be longer, and feature more blood and gore. Examples include a shot of a nurse being gutted and Dr. Wynn being beheaded. Wynn's death was cut out of the film, so that his character could return in future films.

Producer's Cut also expands on certain scenes in the movie. This includes the following:
There are no "flashes" to previous / upcoming scenes throughout the movie, as with the theatrical release.
More dialogue between Loomis and Wynn when Wynn visits Loomis at his house. Wynn asks Loomis why he is "listening to this jerk" Barry Simms, and Loomis says he's recording it because it's a program about Haddonfield. He then goes on to say that he recently had plastic surgery, to remove some of the scarring on his face and "not frighten little children anymore". Then Wynn announces his plan to retire, thus bringing on the toast to "old friends".
More dialogue playing over the radio during this scene. There are also a number of different callers than in the theatrical release.
Kara performs a "chant" for Danny when he has his nightmare. She warns the "evil spirits" to stay away and reminds them that they "know the rules".
An extra scene of Debra and John watching Kara through the window as she leaves for college. Debra says "it's not about her, John... it's about you", and that she doesn't care what Kara has done in the past because she's their daughter. John replies by saying that Kara is no longer his daughter.
The scene with Dawn (Wynn's secretary) telling Loomis and Wynn that Jamie Lloyd's body has been found is extended. Wynn tells her to put the sanitarium on a "Code Red Lock-down" for 24 hours, and then says to Loomis that if Michael is alive, he plans on "bringing him back to Smith's Grove".
The scene where Loomis and Wynn drive to the farm is also extended. Because Jamie survives Michael's initial attack in this version, she is taken to hospital, and Loomis blames himself for everything as she is wheeled to an ambulance. He also has an encounter with the new Sheriff, who tells him that he and Wynn have "no business in Haddonfield", and to go back to their "loony bin".
There are a few alternate angles during the scene where Debra finds out whose house they are really living in. Loomis goes into more detail about Michael, and when Debra is on the phone to John, there are again some alternate angles. Also, when she drops the phone, the dial tone can be heard, whereas it can't in the theatrical release.
Barry Simms' death is also done slightly different. There a couple of alternate angles, and a scene after he is stabbed with the camera panning away to show another van parked nearby with the words "WKNB Radio" on the hood.
There are more alternate angles when Tommy finds Barry's body. The little girl dancing under the tree also sings "it's raining red" instead of saying it.
The ending credits are also completely different, with a few changes to the cast list as well.

Deleted scenes seen only in the Producer's Cut: Michael is shown impregnating Jamie in a black and white flashback, it shows the man in black forcing Michael to do it. In the finale Kara is tied up to an altar while the Thorn cult performs a ritual, Kara says "The baby is yours isn't it Michael?!" and the man in black turns and yells "Michael!." Originally this was the setup for Michael to kill the members of the Thorn cult.

The theatrical version ends with Loomis re-enterting the asylum, and we see Michael's body is gone and we hear Loomis scream, suggesting Michael killed him. In the producer's cut, we see Loomis come across Michael's body, suddenly the mask is pulled off to reveal it is Wynn, who passes on his curse of being Michael's guardian to Loomis before he dies. As the rune of thorn appears on Loomis' arm he screams, and the final image is of Michael disguised as the man in black leaving the asylum.

Because of the very different ending in the producer's cut, the dialogue between Wynn and Loomis in Smithsgrove is different, Wynn's outfit was also changed. The theatrical version simply uses Loomis's reaction shots and had Mitch Ryan reading new lines.