I remapped the UV coords based on the spherical projection of the mesh after subdividing, so there should be minimal distortion, especially compared the UV sphere. There is a slightly higher density of vertices where the edges of the cube used to be, but it's small compared to the UV sphere's extreme convergence at the poles.
I should say you do get distortion where the cube faces meet at the edges. May or may not be a problem depending on how your texturing.