Electroencephalogram (EEG) signal analysis is commonly employed to extract information on the brain dynamics. It mainly targets brain status and communication, thus providing potential to trace differences in the brain's activity under different anesthetics. In this article, two kinds of gamma-amino butyric acid (type A -GABAA) dependent anesthetic agents, propofol and desflurane (28 and 23 patients), were studied and compared with respect to EEG spectrogram dynamics. Hilbert-Huang Transform (HHT) was employed to compute the time varying spectrum for different anesthetic levels in comparison with Fourier based method. Results show that the HHT method generates consistent band power (slow and alpha) dominance pattern as Fourier method does, but exhibits higher concentrated power distribution within each frequency band than the Fourier method during both drugs induced unconsciousness. HHT also finds slow and theta bands peak frequency with better convergence by standard deviation (propofol-slow: 0.46 to 0.24; theta: 1.42 to 0.79; desflurane-slow: 0.30 to 0.25; theta: 1.42 to 0.98) and a shift to relatively lower values for alpha band (propofol: 9.94 Hz to 10.33 Hz, desflurane 8.44 Hz to 8.84 Hz) than Fourier one. For different stage comparisons, although HHT shows significant alpha power increases during unconsciousness stage as the Fourier did previously, it finds no significant high frequency (low gamma) band power difference in propofol whereas it does in desflurane. In addition, when comparing the HHT results within two groups during unconsciousness, high beta band power in propofol is significantly larger than that of desflurane while delta band power behaves oppositely. In conclusion, this study convincingly shows that EEG analyzed here considerably differs between the HHT and Fourier method.