SDDM is a display and login session manager for X11. It uses modern technologies like QtQuick for responsive and beatiful interfaces, which allows smooth themes and animated user interfaces.
LightDM is display and login manager for X11/Mir. It's rather lean, integrates with ConsoleKit, PAM or logind. It provides greeter frontends for Gtk, Qt, KDE and a WebKit UI. It also provides remote session (XDMCP, VNC, RDP) connectors.