Several simultaneous EEG-fMRI studies have aimed to identify the relationship between EEG band power and fMRI resting state networks (RSNs) to elucidate their neurobiological significance. Although common patterns have emerged, inconsistent results have also been reported. This study examines the consistency of these correlations across subjects and to understand how factors such as the hemodynamic response delay and the use of different EEG data spaces (source/scalp) influence them. Using three distinct EEG-fMRI datasets, acquired independently on 1.5T, 3T and 7T MRI scanners (comprising 42 subjects in total), we evaluate the generalizability of our findings across different acquisition conditions. We found consistent correlations between fMRI RSN and EEG band-power time-series across subjects in the three datasets studied, with systematic variations with RSN, EEG frequency-band, and HRF delay, but not with EEG space. Qualitatively, the majority of these correlations were similar across the three datasets, despite important differences in field strength, number of subjects and resting-state conditions. Our findings support consistent correlations across specific fMRI RSNs and EEG bands and highlight the importance of methodological considerations in interpreting them that may explain conflicting reports in existing literature.