A with many movies today, COA has a version of the final cut that has footage not seen in any other formats. The following are scenes that appeared in a Pay Per View version of The Crow: City of Angels, before it was available on video. Souledge316 detailed these on thecrow.com .  There are some variations and additions from scenes seen in the theatrical and video release:

Peep-O-rama scene - After we see Ashe kill Nemo, Kali and Curve arrive at the Peep-o-rama.  As he is about to leave, Ashe looks back to pick up his coat and sees the stripper, Holly Daze. He lifts her up and tells her “leave this place and never look back if you value what is left of your soul”.  As she (Holly) is running out, Curve catches a glimpse of her.
Personal thought - The obvious connection with the Eric/Darla scene from the first movie more than likely was the reason this scene did not make the final theater and video cut.

Kali's death scene – Ashe has thrown Kali out the window. We next see her on the ground, struggling to breath. We see a shadow image of the crow and then a man appears on a wall just away from her. Ashe's feet suddenly appear beside Kali and she asks him to finish her. Instead, Ashe just stares at her and tells her “no, my job was to make you suffer, to send you to hell. You are there”.  The crow then flies off his shoulder down the street and Kali is left there as the crow sign appears in blood.
Personal thought - Not sure why this scene did not make the final theater and video cut. This is one of the more tantalizing scenes from either of the crow movies. The inference that the crow and Ashe are one is very intriguing.

Ashe's fall from the tower- After Ashe falls from the tower and lands in the flowers, Danny appears and tells him that “it is time to go”. The sky is then shown, crows everywhere. Ashe reponds to Danny saying “I cant go, I can not leave  Sarah here”. Danny tells Ashe “if you stay, we will never be together.”  Danny leaves and Ashe screams for him.
Personal thought - This again is a case where I am confused as to why this added section of the scene was left out of the theater and video release. Just the little bit more of dialogue between Ashe and Danny helps to give the audience a better feel for the emotions going through Ashe at the time. As with many scenes, the audience was left to figure out these emotions on their own. 

Sarah's death scene - After Judah has been taken away by the crows, Ashe turns around to Sarah. He kneels down beside her and says; “you can not die, I stayed her for you.”  Sarah responds; “I believe if two people are meant to be together that nothing will keep them apart, not even death”.  Sarah then gives Ashe her ring and tells him; “I will  wait forever for you.” Sarah then dies and Ashe sees the painting she was working on appear in her eyes.
Personal thought - Not to sound like a broken record, it is very puzzling why the theater and video lacked this extra dialogue. The love between Ashe and Sarah is better represented in this scene than any of the others that remained in the final cut of the theater and video versions.

Ending scene -Ashe carries Sarah's lifeless body to the church. Once there, he lays her at the front of the shrine of candles and sits down, hoping she will wake up. The priest from an earlier scene comes close to Ashe and asks him; "what will you do now my son?".  Ashe responds; "I do not know father, this city is full of shadows, one more will not make it any darker". Ashe turns and exits the church. He climbs aboard his motorcycle and leaves.
Personal thought – This scene, more than likely, was not included in the theater and video versions to keep confusion by the audience to a minimum, not to mention it was not what you would call a “Hollywood” ending. The novelization ends in this same fashion, but also includes dialogue prior to the scene that better helps you understand why he (Ashe) has not moved on. It was the original premise of the film that since Sarah died, she took his place in the land beyond (remember the comment that the crows were there to take someone?). My thinking is since the audience was not given this information, along with other dialogue, the ending described above would have been very confusing.