Functional connectivity (FC) metrics describe brain inter-regional interactions and may complement information provided by common power-based analyses. Here, we investigated whether the FC-metrics weighted Phase Lag Index (wPLI) and weighted Symbolic Mutual Information (wSMI) may unveil functional differences across four stages of vigilance-wakefulness (W), NREM-N2, NREM-N3, and REM sleep-with respect to each other and to power-based features. Moreover, we explored their possible contribution in identifying differences between stages characterized by distinct levels of consciousness (REM+W vs. N2+N3) or sensory disconnection (REM vs. W). Overnight sleep and resting-state wakefulness recordings from 24 healthy participants (27 ± 6 years, 13F) were analyzed to extract power and FC-based features in six classical frequency bands. Cross-validated linear discriminant analyses (LDA) were applied to investigate the ability of extracted features to discriminate (1) the four vigilance stages, (2) W+REM vs. N2+N3, and (3) W vs. REM. For the four-way vigilance stages classification, combining features based on power and both connectivity metrics significantly increased accuracy relative to considering only power, wPLI, or wSMI features. Delta-power and connectivity (0.5-4 Hz) represented the most relevant features for all the tested classifications, in line with a possible involvement of slow waves in consciousness and sensory disconnection. Sigma-FC, but not sigma-power (12-16 Hz), was found to strongly contribute to the differentiation between states characterized by higher (W+REM) and lower (N2+N3) probabilities of conscious experiences. Finally, alpha-FC resulted as the most relevant FC-feature for distinguishing among wakefulness and REM sleep and may thus reflect the level of disconnection from the external environment.