The original Broadway production actually started off-Broadway.
It opened at the Cherry Lane Theatre in May of 1971 and moved to the larger Promenade that August, where it played until 1976,when it moved to the Broadhurst, Plymouth and Ambassador theaters on Broadway for another year or so.
How is the music different from the original to the 2001 touring? Well, the melodies are the same, the bones of the arrangements are kind of there on some of the songs, but that's about it. I saw that production and thought it was awful and tried way too hard to update the piece in every possible way. The set was ugly, the arrangements were often laughable (especially in Turn Back O Man), and the ending, was ultimately unmoving-which is very hard to accomplish in Godspell. I did not see the off-Broadway production that took place in the early 2000's (with Foa, Bean, Kimball etc.), but I own the CD and they did a really nice job there with updating the music just enough to give it a fresh sound, yet kept very faithful to the original arrangements. If you're trying to decide between versions on CD, I'd recommend the original first, then the off-Broadway revival, and then the movie soundtrack, which I'm a big fan of.
"Y'all have a GRAND day now"