Nintendo looking into Wii U to Wii U transfers
Right now, content can only be transferred from a Wii to Wii U. Moving data from one Wii U to another is currently impossible.
Fortunately, Nintendo is looking into such functionality. The feature would presumably work similar to 3DS transfers if/when it were to be made available.
According to a Q&A excerpt from Nintendo’s support site:
I know games can be transferred from a Wii to a Wii U, but how about from a Wii U to a Wii U?
Transferring data from one Wii U to another Wii U is not supported at this time. However, we are looking into this feature and will provide an update if there is anything to report.If I bought a Basic console and purchase games from the Nintendo eShop, and then buy a Deluxe console and want to transfer those games, is that possible?
Transferring data from one Wii U to another Wii U is not supported at this time. However, we understand that this is a feature of interest to some consumers so we are taking that into consideration and are looking into this feature.