It will depend on the generations from both FANUC and KUKA controllers.
On FANUC, in most cases You can setup an FTP connection and download from there.
On KUKA, if Your robot controller is KRC4 or above, you can setup the robot to make a backup on a remote folder, or just use WorkVisual to make network backups. Previous generations doens't work with WorkVisual, but offer the option of network backups, in a way or another.