Differences between the Gamecube and the Wii version of Twilight Princess

The main difference is that the whole game is flipped, horizontally. In the Game Cube version, Link is left handed (as he was in all previous games). In the Wii version, he is right handed. In order to avoid re-doing all of the graphics in the game, they just flipped the entire game - Lake Hylia is in the southeast corner instead of the southwest corner, if there is a path to the left in the Game Cube version, it is to the right on the Wii, etc.

I recall that Nintendo stated that this had something to do with players using the Wiimote in their right hand, and the interaction with the game was odd if Link was left handed, but I'm not positive on that.

The Wii version doesn't have free camera mode - on the GC version you can use the C-stick to move your camera around while running and stuff.

Also I find that just holding B to release a spin attack is much more reliable than using the nunchuk/ Wiimote combo.

According to Wikipedia, they were released at the same time, mainly just with a different control scheme. However, since most people are right-handed, and Link was left-handed in the GC version, they decided to flip the entire world, changing West to the East and East to the West. So, just watch out for that when using a Walkthrough or trying to play on multiple versions.