I caught a great HD presentation of this movie on cable a few years ago at like 2 in the morning, but didn't record it. I do remember, however, taking notes of the songs differences.
Basically put, when you see bad vhs/laserdisc copies of the movie (usually on youtube or a torrent), most of the music is score music written and performed by Eddie Van Halen. I thought he did the original music and his music was later replaced because Eddie never signed off on it in regards to distribution releases. However, someone told me that the "alternate" music is the ORIGINAL music, and the Van Halen stuff was added later for vhs/laserdisc release. I can't confirm this though, only one person told me this. But FWIW, it does make sense that the Van Halen score was done 2nd, as it's mostly demo versions of songs they made later with Sammy Hagar.
As a huge Van Halen fan, I think you can all guess which score I prefer ;)
Oh and for those interested, most of those score pieces Eddie wrote are now available on youtube. The full pieces even show parts of the score that wasn't used in the film. I'd post the links the proper way, but the insert/edit link button isn't working for me for some reason.
The song when the guys are cruisin' the blvd.
http://www.youtube.com/watch?v=183gpii_ans
The song when the cop investigates the explosion at the school (Demo version of "Good Enough")
http://www.youtube.com/watch?v=8Dw6YrpsPWs
The end credits music. Basically a b-side instrumental version of "Jump".
http://www.youtube.com/watch?v=rgMfaRdOYnM
The piece that was used in Back to the Future:
http://www.youtube.com/watch?v=zmc6f2kCyLU
And of course, the track that Eddie recently re-used (or "properly finished" if you prefer to use that terminology) for the new VH album:
http://www.youtube.com/watch?v=qe1X3yOWhdA
They haven't released ALL the pieces used in the film yet. There's still the demo versions of "Mine, All Mine", "Right Now", and "Naturally Wired". Hopefully they'll release them to someday.