The Wii version supports 480p resolution while the GameCube version only supports 480i resolution, if you have a TV that can support 480p or higher, and component cables instead of composite cables.
The Wii version has widescreen and the GC version doesn't, so your items and health can be way out of the way of the actual playfield.
The Wii's IR controls for the bow, slingshot, boomerang, and hookshot are far superior than aiming with an analog stick on a GC controller. You can do it much faster by pointing, which is really helpful for a couple fights.
The Wii's tilting controls for fishing, flying, snowboarding, and the RollGoal minigame are far superior than using an analog stick on a GC controller.
I'd say go with the Wii version, unless, as Rol said, you might just be a button type of guy.
But I preferred the motion controls for combat as well 'cuz you can use one hand for the sword and one hand for the shield, and I can't stand having my hands glued together anymore, unless I'm using a giant battle axe or something.
Gameplay-wise, you can expect a slow introduction followed by tons of exploring, tons of combat, tons of puzzles, tons of minigames, tons of secrets, and tons of ghosts.