New Region One blu-ray from Mondo-Vision is simply gorgeous

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The cut is the same, but the soundtrack is different. Mondo Vision decided to include both tracks and they labeled the one from Anchorbay Disc as "Unauthorized Alternate Audio track"

Found this post on Blu-ray forum which explains the story behind the Unauthorized Alternate Audio track:
http://forum.blu-ray.com/showthread.php?p=9252741#post9252741

"If you happened to have seen the original Anchorbay Disc from early 2000, this is the audio track that was used over the film. There are many scenes where music plays in the background, the most notable being the subway scene; there shouldn't be any music during that scene. If you flip to the Unauthorized audio you notice it plays the piano theme all the way through it. There are other parts as "Lyris" mentioned too. All the pieces were composed for the film, but Zulawski didn't use them all for the final cut. No one knows how it happened but somewhere down the line someone decided to add those music cues back to the film without Zulawski's permission. Basically any one who bought the Anchorbay disc ended up watching the wrong film! If you bought the LE, refer to the technical sheet, on the OST track list Mondo Vision has clearly marked where each track belongs to.

Taken from the technical sheet:

Tracks marked (green *) appear in the Director Approved Final Cut of the film.
Tracks marked (red *) appear in the Unauthorized Alternate Audio track. (See Note)
Tracks marked (black *) are Previously Unreleased.

Note: A handful of releases, including POSSESSION’s first U.S. DVD release (ironically billed as the “Director’s Cut”) were issued with an Unauthorized Alternate Audio track consisting of additional music. This additional music was composed by Andrzej Korzyñski but omitted by the director in the final cut of the film."