The complaints of people suffering from Insomnia Disorder (ID) concern both sleep and daytime functioning. However, little is known about wake brain temporal dynamics in people with ID. We therefore assessed possible alterations in Long-Range Temporal Correlations (LRTC) in the amplitude fluctuations of band-filtered oscillations in electroencephalography (EEG) recordings. We investigated whether LRTC differ between cases with ID and matched controls. Within both groups, we moreover investigated whether individual differences in subjective insomnia complaints are associated with LRTC. Resting-state high-density EEG (256-channel) was recorded in 52 participants with ID and 43 age- and sex-matched controls, during Eyes Open (EO) and Eyes Closed (EC). Detrended fluctuation analysis was applied to the amplitude envelope of band-filtered EEG oscillations (theta, alpha, sigma, beta-1, beta-2) to obtain the Hurst exponents (H), as measures of LRTC. Participants rated their subjective insomnia complaints using the Insomnia Severity Index (ISI). Through general linear models, we evaluated whether H, aggregated across electrodes and frequencies, differed between cases and controls, or showed within-group associations with individual differences in ISI. Additionally, we characterized the spatio-spectral profiles of group differences and associations using non-parametric statistics. H did not differ between cases with ID and controls in any of the frequency bands, neither during EO nor EC. During EO, however, within-group associations between H and ISI indicated that individuals who experienced worse sleep quality had stronger LRTC. Spatio-spectral profiles indicated that the associations held most prominently for the amplitude fluctuations of parietal theta oscillations within the ID group, and of centro-frontal beta-1 oscillations in controls. While people suffering from insomnia experience substantially worse sleep quality than controls, their brain dynamics express similar strength of LRTC. In each group, however, individuals experiencing worse sleep quality tend to have stronger LRTC during eyes open wakefulness, in a spatio-spectral range specific for each group. Taken together, the findings indicate that subjective insomnia complaints involve distinct dynamical processes in people with ID and controls. The findings are in agreement with recent reports on decreasing LRTC with sleep depth, and with the hypothesis that sleep balances brain excitability.