I present a systematic evaluation of different types of metrics, for inferring magnitude, amplitude, or phase synchronization from the electroencephalogram (EEG) and the magnetoencephalogram (MEG). I used a biophysical model, generating EEG/MEG-like signals, together with a system of two coupled self-sustained chaotic oscillators, containing clear transitions from phase to amplitude synchronization solely modulated by coupling strength. Specifically, I compared metrics according to five benchmarks for assessing different types of reliability factors, including immunity to spatial leakage, test-retest reliability, and sensitivity to noise, coupling strength, and synchronization transition. My results delineate the heterogeneous reliability of widely used connectivity metrics, including two magnitude synchronization metrics [coherence (Coh) and imaginary part of coherence (ImCoh)], two amplitude synchronization metrics [amplitude envelope correlation (AEC) and corrected amplitude envelope correlation (AEC)], and three phase synchronization metrics [phase coherence (PCoh), phase lag index (PLI), and weighted PLI (wPLI)]. First, the Coh, AEC, and PCoh were prone to create spurious connections caused by spatial leakage. Therefore, they are not recommended to be applied to real EEG/MEG data. The ImCoh, AEC, PLI, and wPLI were less affected by spatial leakage. The PLI and wPLI showed the highest immunity to spatial leakage. Second, the PLI and wPLI showed higher test-retest reliability and higher sensitivity to coupling strength and synchronization transition than the ImCoh and AEC. Third, the AEC was less noisy than the ImCoh, PLI, and wPLI. In sum, my work shows that the choice of connectivity metric should be determined after a comprehensive consideration of the aforementioned five reliability factors.