Everything or saves or nothing will be transferred. Using the program
here, you can transfer everything, with the keys.bin of one Wii and the nand.bin of another. Here's how.
1. Transfer the first Wii's keys.bin and the 2nd Wii's keys.bin to your PC
2. Launch the exe
3. Extract the files to a folder on your desktop
4. Run the app
5. Launch the first dialogue box
6. Navigate to the 1st Wii's keys.bin file
7. On the next dialogue box, navigate to the second Wii's keys.bin
8. Copy the first Wii's nand.bin to /appfolder/betwiin/input
9. Click on convert and answer the prompts.
10. When finished, take the nand.bin from /appfolder/betwiin/input, and move it to your SD card.
11. Take your SD card and put it in the 2nd Wii.
12. Restore that nand.bin with BootMii.
Savegames will work, but
purchased WiiWare won't work, nor can you redownload them. You must create a new Shop Channel account and start from scratch on the new Wii.
That's it!
Note that the version of boot1 on both Wii's must be the same.