Paradox of two fluid planets in an uniform rotation

This is a striking paradox described by Einstein in his classical work on general relativity (1916).
He attributed it to Ernst Mach, but I could not find the exact description of it in Mach's History of Mechanics.
Paradox of two fluid planets.
Two fluid planets of the same size and nature hover freely in space at so great a distance from each other that only those gravitational forces need be taken into
account which arise from the interaction of different parts of
the same planet. There are no other bodies is the space!
Let the distance between the two planets be invariable, and in neither of the planets let there be any relative movements of the parts with respect to one another.
But let either mass, as judged by an observer at rest relatively to the other mass, rotate with constant angular velocity about the line joining the masses.
This is a verifiable relative motion of the two bodies. From experience we know that rotating fluid sphere becomes an ellipsoid due to centrifugal forces.
Now the question is: which planet has an elliptical form and which has a spherical?
What is the reason for the difference in these two planets?