The only difference I would pressume is slightly higher quality materials and the like, but that's probably not true. Possibly a higher system menu version than used or older white Wiis; which is easily obtained by wi-fi connection regardless. So I'd assume there's no important difference, and probably not any difference at all.
This goes back to when Nintendo released the Color Gameboy; not the Gameboy Color, but the Color Gameboy. It was the same Gameboy Pocket everyone owned, but with different color casing. It sold heaps regardless of having no changes but the color.