Generally, they changed many things; for example, the statues in Sorpigal were changed to plaques,
you can't leave Sorpigal until you're level 2, A guild that can change character classes was added,
healing, reviving and removing curses are cheaper, an automap was added, along with differences in the plot.
Also, specifically for the US release, attacks are gained every 4 levels instead of 8 (probably to reflect
Might and Magic 2) various monster names were changed most likely out of censorship or flawed translation,
and battle animations were added/removed.
Also, it seems like running at the beginning of battle works, and your characters appear stronger, but slower
in the US version, because monsters get in attacks before you do.