kdesu, at least as used in my Gnome menu for the Install Software link (which is its own bug, 244442), asks for the root password. However, it does not accept the root password when entered. Instead, it accepts my user password. Presumably this is because it uses sudo and my sudoers file is configured to let me do anything as root by providing my own password. That's no excuse. The dialog must ask for the password that it will accept.

For a non-sudoer user, neither the user's nor root's password is accepted.

Meanwhile, gnomesu asks for the root password and accepts the root password (even for a non-sudoer user). The two should operate the same way on a given system.