A growing body of evidence suggests that the neuronal dynamics are poised at criticality. Neuronal avalanches and long-range temporal correlations (LRTCs) are hallmarks of such critical dynamics in neuronal activity and occur at fast (subsecond) and slow (seconds to hours) timescales, respectively. The critical dynamics at different timescales can be characterized by their power-law scaling exponents. However, insight into the avalanche dynamics and LRTCs in the human brain has been largely obtained with sensor-level MEG and EEG recordings, which yield only limited anatomical insight and results confounded by signal mixing. We investigated here the relationship between the human neuronal dynamics at fast and slow timescales using both source-reconstructed MEG and intracranial stereotactical electroencephalography (SEEG). Both MEG and SEEG revealed avalanche dynamics that were characterized parameter-dependently by power-law or truncated-power-law size distributions. Both methods also revealed robust LRTCs throughout the neocortex with distinct scaling exponents in different functional brain systems and frequency bands. The exponents of power-law regimen neuronal avalanches and LRTCs were strongly correlated across subjects. Qualitatively similar power-law correlations were also observed in surrogate data without spatial correlations but with scaling exponents distinct from those of original data. Furthermore, we found that LRTCs in the autonomous nervous system, as indexed by heart-rate variability, were correlated in a complex manner with cortical neuronal avalanches and LRTCs in MEG but not SEEG. These scalp and intracranial data hence show that power-law scaling behavior is a pervasive but neuroanatomically inhomogeneous property of neuronal dynamics in central and autonomous nervous systems.