The neural processes underlying attentional processing are typically lateralized in adults, with spatial attention associated with the right hemisphere (RH) and object-based attention with the left hemisphere (LH). Using a modified two-rectangle attention paradigm, we compared the lateralization profiles of individuals with childhood hemispherectomy (either LH or RH) and age-matched, typically developing controls. Although patients exhibited slower reaction times (RTs) compared to controls, both groups benefited from valid attentional cueing. However, patients experienced significantly higher costs for invalid trials—reflected by larger RT differences between validly and invalidly cued targets. This was true for invalid trials on both cued and uncued objects, probes of object- and space-based attentional processes, respectively. Notably, controls showed no significant RT cost differences between invalidly cued locations on cued versus uncued objects. By contrast, patients exhibited greater RT costs for targets on uncued versus cued objects, suggesting greater difficulty shifting attention across objects. We explore potential explanations for this group difference and the lack of difference between patients with LH or RH resection. These findings enhance our understanding of spatial and object-based attention in typical development and reveal how significant neural injury affects the development of attentional systems in the LH and RH.