Nintendo has revealed that Zelda: Breath of the Wild will be 13.4gb on the Nintendo Switch and 13gb on the Nintendo Wii U. Considering that the Switch has 32gb of inbuilt memory, this is a sizeable chunk taken up on Zelda if you’re going digital.
Nintendo has also revealed that at launch, Nintendo Switch carts will have a maximum of 16gb storage. This could be increased with time, as it was with the Nintendo 3DS.
It has been confirmed that saves will be stored on the actual system memory rather than on carts which has been the way with previous Nintendo cartridges.