The WiiWare version will feature a number of changes, partly to tone down the difficulty and improve design in order to appeal to a larger audience, partly to give players who've played the original a new experience, and partly due to copyright issues. In addition, the graphics will be updated to a smoother style and the music will come in orchestrated form.
The last category includes such changes as:
Renaming the MSX computer system the "Mobile Super X".
A revision to the melody of "Curse of IRON PIPE" in order to remove similarities with a certain track from the game Ashguine II.
Source: Wikipedia, "La Mulana", available under the CC-BY-SA License.