I'd say the definitive version is the original fan-translated Windows version. However, for the most part I actually prefer Cave Story+. It's been ported to multiple platforms, it's more convenient, and you can switch between new and original graphics and music. The new graphics I thought were stylistically very faithful to the original, but I'd recommend using the original music, as what little I'd heard of the new didn't seem to capture its charm.

The one thing I don't like about Cave Story+ is how it messes with the player graphics under certain circumstances. The first time I started up the game, my guy looked like a reindeer, apparently because it detected that I was playing it during the holidays or something. Not a big deal, but kind of annoying since there doesn't seem to be any way to turn it off. It also changes the way your guy looks depending on the difficulty level you choose. Other than that, great version IMO.