Prematurely born children are at higher risk for long-term adverse motor and cognitive outcomes. The aim of this paper was to compare quantitative measures derived from electroencephalography (EEG) between extremely (EP) and very prematurely (VP) born children at 9–10 years of age. Fifty-five children born <32 weeks' of gestation underwent EEG at 9–10 years of age and were assessed for motor development and cognitive outcome. Relative frequency power and functional connectivity, as measured by the Phase Lag Index (PLI), were calculated for all frequency bands. Per subject, power spectrum and functional connectivity results were averaged over all channels and pairwise PLI values to explore differences in global frequency power and functional connectivity between EP and VP children. Brain networks were constructed for the upper alpha frequency band using the Minimum Spanning Tree method and were compared between EP and VP children. In addition, the relationships between upper alpha quantitative EEG results and cognitive and motor outcomes were investigated. Relative power and functional connectivity were significantly higher in VP than EP children in the upper alpha frequency band, and VP children had more integrated networks. A strong positive correlation was found between relative upper alpha power and motor outcome whilst controlling for gestational age, age during EEG recording, and gender (ρ = 0.493, p = 0.004). These results suggest that 9–10 years after birth, the effects of the degree of prematurity can be observed in terms of alterations in functional brain activity and that motor deficits are associated with decreases in relative upper alpha power.