To add to other answers there is one badass of a thing that you can do on Gamecube version and not on Wii version  :

Load your spin attack while on Epona's back. Wich makes Link raise it's arm and sword in a very nice stylish effect, with some sparkle going along the sword. When charging toward enemies with the B button pushed it gave some LOTR felling that i regret they removed from Wii version

To add to other answers, there is one badass thing that you can do on Gamecube version, but not on Wii version:

Try loading your spin attack while on Epona's back. This makes Link raise his arm and sword in a very nice, stylish effect, with some sparkle going along the sword. When charging toward enemies with the B button pushed, it felt like some LOTR vibes that I wish they hadn't removed from Wii version.