Zelda: Breath of the Wild's Wii U Version Has a 3 GB Install
The new Zelda game requires storage space on Wii U whether you download it or pick up a disc.
Anyone opting to pick up the disc version of The Legend of Zelda: Breath of the Wild on Wii U will be faced with a mandatory installation, though it won't require quite as much space as the digital version.
According to the Nintendo of Japan page for the game (via Nintendo Everything), a select amount of data needs to be installed to the system or an external storage device. Specifically, you'll need to install 3 GB's worth of data to play the game. It's unclear what exactly this is for or if, like with Xenoblade Chronicles X, there will be additional, optional files you can install to expedite load times.
By contrast, the digital version of Breath of the Wild on Wii U takes up 13 GB. The digital Switch version requires 13.4 GB, which is a fairly substantial portion of the system's internal storage. Its capacity can be expanded with microSDXC cards, while the Wii U allows you to use an external USB hard drive.