Performing a task across the left and right visual hemifields results in better performance than in a within-hemifield version of the task, termed the different-hemifield advantage. Although recent studies used transient stimuli that were presented with long ISIs, here we used a continuous objective electrophysiological (EEG) measure of competitive interactions for attentional processing resources in early visual cortex, the steady-state visual evoked potential (SSVEP). We frequency-tagged locations in each visual quadrant and at central fixation by flickering light-emitting diodes (LEDs) at different frequencies to elicit distinguishable SSVEPs. Stimuli were presented for several seconds, and participants were cued to attend to two LEDs either in one (Within) or distributed across left and right visual hemifields (Across). In addition, we introduced two reference measures: one for suppressive interactions between the peripheral LEDs by using a task at fixation where attention was withdrawn from the periphery and another estimating the upper bound of SSVEP amplitude by cueing participants to attend to only one of the peripheral LEDs. We found significantly greater SSVEP amplitude modulations in Across compared with Within hemifield conditions. No differences were found between SSVEP amplitudes elicited by the peripheral LEDs when participants attended to the centrally located LEDs compared with when peripheral LEDs had to be ignored in Across and Within trials. Attending to only one LED elicited the same SSVEP amplitude as Across conditions. Although behavioral data displayed a more complex pattern, SSVEP amplitudes were well in line with the predictions of the different-hemifield advantage account during sustained visuospatial attention.