The time difference, not counting the credits, is 107 seconds.
"Wicked City" is a typical anime of the 80s and 90s. Those can be characterized especially by their standardized (loveless) style of drawing and the way the animations were done. As also very typical for that time, this anime is a mixture of Action, spooky-fantasy with a few erotic scenes. But those were apparently too explicit for the release in UK and thus were partially removed. The "hardest" parts of the soft scenes were removed. Yet, the scenes never become explicit at any moment. You never see genitalia or alike, yet the scenes are unmistakable.
The movie doesn't really suffer from the cuts, if some of them weren't done so badly obvious. Plus the scenes that were removed aren't really harder than the scenes that have been left intact, which gives us the question why those cuts were thought to be necessary.
Besides that the US and the UK version are differently dubbed. The UK version stands out due to the use of far more curses. The best example can be given in the scene where the plane explodes. In the US version Taki says "What...? But how...?", while in the UK version he yells "Fuck!". The content of the dialogues is all in all the same though. The choice of voiceactors is in both versions partially very good and partially very bad. Yet you can watch both versions without any "pain" in the ears. The score is mostly the same, only in a few scenes it was changed.
Another interesting detail when it comes to the UK dubs is a scene in the middle of the movie. Makie, the female main character, is held captive and being raped. While we only hear a dull moaning in the US version, the moaning is clearly louder in the UK version. Besides that we can hear Makie scream and beg ("No! Please don't!") in the UK version. Apparently it didn't occur to the persons in charge for the british version, that this different dub makes this scene harder then it is in the US version.
Although the US version is to be preferred just because it's uncensored, the question can be asked how it comes that the picture is so abnormally dark that words can't describe it. At some scenes you just can't see anything, because the picture is too dark. Compared to the UK video the colors are stronger and have mor contrast, but that is no excuse. At some parts there was even a complete different coloring.
(in general for comparisons: left US, right UK cut version)
The intro was changed slightly. In the US version the camera starts with a bigger distance to the city, while the skyline is very close in the UK version. The zoom-out in the US version is slower for that. At the end both versions come to the same "spot". Also the narrator's monologue starts a bit later in the US version.
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The title was changed.
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The camera drives over Makie, who is held down by Jin. Jin has his hand in der panties.
Close shot to Jin's hand in Makie's panties, then Makie's hairs start slowly to float.
Makie slams her fingers into her breast. The demon opens her mouth with his tentacle and slams it into it. The tentacle is moving for- and backward and the camera changes from an internal shot to Makie's face a few times. Finally Makie's eyes begin to glow and enegery starts to shoot out of the holes in her breast.
In the UK version the sign (Spiritual Healing Centre) was translated, in the US version not.
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The last two parts of Taki's vision, where he sees Makie being raped by demons, was removed.
More parts of the vision are shown.
Demon (Off): "Look what we do with traitors. She was someone from the dark world, but she helped creating these peace treaties. A peace only humans can believe in. Besides that she killed her former lover."
Again we see part of Taki's vision.
Mayard (Off): "You can say she has called it up on herself. She could have been nicer to me when she had the chance. But she messed it up."
Some scenes are shown as the three demons rape Makie.
Demon (Off): "Hehehe... so the blackguard has it's appearance."
A part of what the demon is saying to Taki was removed. Also the UK version misses most of the following scene. It starts again when the camera has zoomed out very far and you can't really tell what's happening to Makie anymore.
Demon: "I'm sure you can't wait to hold her in your arms again, can you?"
Taki: "You son of a bitch."
Demon: "Hehehe... yeah, thanks. Before we proceed with the festivities there are some things I have to know. For example if you are a real man."
The credits were slightly changed. The US version shows freeze frames from the movie, while the UK version shows the city colored in red tones.