A very interesting question! Of course, we know that the dopaminergic (DA) and noradrenergic (NE) systems are represented in the two hemispheres in a somewhat different ways. Furthermore, the NE system (somewhat more prolific in the right than in the left hemisphere) is particularly closely linked to the regulation of sleep-wake cycle. So it would appear that any alterations of the arousal level would affect the right hemisphere more. This is a conjecture, but one readily amenable to experimental validation.

EG