The main advantage over using active stabilization with propellants, gyroscopes or reaction wheels is the low use of power and resources.
[1] The technique exploits the Earth's gravitational field and tidal forces to keep the spacecraft aligned along the desired orientation.
The effect is that the satellite will tend to align its axis of minimum moment of inertia vertically.
[4] The lunar orbiter Explorer 49 launched in 1973 was gravity gradient oriented (Z axis parallel to local vertical).
[6]: 7 Gravity-gradient stabilization was attempted during NASA's TSS-1 mission in July 1992, but the project failed due to tether deployment problems.