Other examples:
Aladdin - Sega did the Genesis version working with Disney and Capcom did the SNES version. Both were good games, but the Genesis version is generally lauded as superior due to it's animation/art style. However, the SNES definitely can pump out music that's more authentic to the source.

Earthworm Jim and Cool Spot were both originally programmed for the Genesis and then ported to the SNES. This results in a more zoomed in view in the SNES version as the Genesis is running at either 320x240 or 320x224 (I can't remember what it does off the top of my head) while the SNES versions run at their standard 256x224 resolution. If I recall correctly, Earthworm Jim 2 is superior on the SNES as I *think* it was the original version for ports.