The stronger side suppresses the weaker side more, sharpening the lateral asymmetry.

Evidence

Because the stimulus level was higher on the left ear, the output amplitude was also higher for the leftthan for the right-ear MOC processor. Hence, the left-ear MOC processor inhibited the right-ear MOC processor more than the other way around. — Dijk, Pim van, Physiology, Psychoacoustics and…, 1961