First let me say there are two English dubbed versions of this movie. The first version is a faithful translation of the original complete with all the original scenes. Overall the first version is actually more exciting because of the music - the music makes all the actions scenes more heart-pounding and is an excellent example of how sound can affect a scene. I found the current US-released English version less of an adrenaline rush because of the droll music in the action scenes.
Furthermore, I found the original English-dubbed version much funnier. There's something charming about the original text - Jackie is actually more arrogant and aloof in the original version, and it helped create a more exciting "mercenary" feel to Jackie's character, rather than the more confusing humanitarian/treasure-hunter feel to the new version. Jackie treats Alan Tam's character more harshly and with some funny sarcastic comebacks. In the new version, the witty come-backs were replaced with patient words!
Lastly, the most notable change in the new version is the entire "Lorelei wants the armour in the house" scene is entirely missing. In the original version, May goes to Jackie's room to look at his baby pictures (Jackie asks May to look at them to get out of the situation where he and Alan were caught in May's bedroom), and both of them are shocked to see Lorelei on his bed. May storms off in disgust. Meanwhile Lorelei goes into the bathroom to prepare the serum, and Alan walks into the bedroom. Jackie has to cover Lorelei and lies to Alan that it is May that is in the bathroom. Both Jackie and Alan go out into the hall and bump into May, and Jackie has to cover his tracks by pretending that Alan knows that Lorelei is in Jackie's bedroom. Naturally May responds with disgust that "they are such good friends that they share everything, even girlfriends". Then Alan gets suspicious because May was in the hall not the bathroom, he goes into Jackie's bedroom to see if the bathroom is connected to May's bedroom, and then gets jabbed by Lorelei (which is where the new version cuts back in).
The new version is a more streamlined version, and certainly the story flows better. There is actually a romance between May and Jackie which I prefer, whereas in the original version May remains angry with Jackie after she slaps him and they never get past that stage - especially after she gets the impression that Jackie "shares" Lorelei with Alan!
I was really disappointed, because I had the original English-dubbed version and it was one of my all-time favourite Jackie Chan movies because of Jackie's arrogant character which was a huge departure from the usual benevolent roles that Jackie plays, and because of the music which really made the difference in the action scenes for me. Alas, my original version was a video tape that grew fungus and was therefore ruined - and I have no idea how to get that version again!
Jackie's voice in the original English version was dubbed by someone else (the same person that dubbed the English versions for all his movies in the 80s) - and it sounds a lot better than Jackie's real voice which he uses in the new version. Funny thing is the voices actually sound alike sans accent.
