Visuospatial attention theories often propose hemispheric asymmetries underlying the control of attention. In general support of these theories, previous EEG/MEG studies have shown that spatial attention is associated with hemispheric modulation of posterior alpha power (gating by inhibition). However, since measures of alpha power are typically expressed as lateralization scores, or collapsed across left and right attention shifts, the individual hemispheric contribution to the attentional control mechanism remains unclear. This is, however, the most crucial and decisive aspect in which the currently competing attention theories continue to disagree. To resolve this long-standing conflict, we derived predictions regarding alpha power modulations from Heilman's hemispatial theory and Kinsbourne's interhemispheric competition theory and tested them empirically in an EEG experiment. We used an attention paradigm capable of isolating alpha power modulation in two attentional states, namely attentional bias in a neutral cue condition and spatial orienting following directional cues. Differential alpha modulations were found for both hemispheres across conditions. When anticipating peripheral visual targets without preceding directional cues (neutral condition), posterior alpha power in the left hemisphere was generally lower and more strongly modulated than in the right hemisphere, in line with the interhemispheric competition theory. Intriguingly, however, while alpha power in the right hemisphere was modulated by both, cue-directed leftward and rightward attention shifts, the left hemisphere only showed modulations by rightward shifts of spatial attention, in line with the hemispatial theory. This suggests that the two theories may not be mutually exclusive, but rather apply to different attentional states.