Well this would be hard as i have only played the Wii and PC version. If i had to choose between these two i would pick the original. And my reasons are:
1.Mod Support: though its pretty minor and i hear cave story + also has it.
2.The Translation: Huzzah!
3.Controls: The PC version has a bigger list of controllers. And if i dont have any the keyboard is still very comfortable. Much better than the small d-pad the wii uses.
And: i must agree with Miles when it comes to the game being good for it being the gift of a man, to quote him: "Not to mention when Pixel made this original Cave Story, on his own... It was a personal project. He wasnt thinking about money, popularity or business. Cave Story has a certain intimacy to it that no other version will equal because it's so genuinely a man pouring his heart into a game for the sake of the game".
I have a few more reasons but that would just be repeating what every one has already said on the topic.