The backup file is a standard tar archive so take a copy and see if it unpacks on your desktop OS first. If it has a problem there; it's damaged in some way. If it's okay there is some other problem but you should be able to copy the file to the new SD card and just 'untar' the file somewhere else, e.g.
systemctl stop kodi
rm -rf /storage/.kodi /storage/.cache /storage/.config
tar -xvf backupfile.tar
The archive contains paths so it will overwrite the current folders, hence ^ removing them first.