pi-Conjugated two-dimensional covalent organic frameworks (2D COFs) are emerging as a novel class of electroactive materials for (opto)electronic and chemiresistive sensing applications. However, understanding the intricate interplay between chemistry, structure, and conductivity in pi-conjugated 2D COFs remains elusive. Here, we report a detailed characterization for the electronic properties of two novel samples consisting of Zn- and Cu-phthalocyanine-based pyrazine-linked 2D COFs. These 2D COFs are synthesized by condensation of metal-phthalocyanine (M = Zn and Cu) and pyrene derivatives. The obtained polycrystalline-layered COFs are p-type semiconductors both with a band gap of similar to 1.2 eV. A record device-relevant mobility up to similar to 5 cm(2)/(V s) is resolved in the dc limit, which represents a lower threshold induced by charge carrier localization at crystalline grain boundaries. Hall effect measurements (dc limit) and terahertz (THz) spectroscopy (ac limit) in combination with density functional theory (DFT) calculations demonstrate that varying metal center from Cu to Zn in the phthalocyanine moiety has a negligible effect in the conductivity (similar to 5 x 10(-7) S/cm), charge carrier density (similar to 10(12) cm(-3)), charge carrier scattering rate (similar to 3 x 10(13) s(-1)), and effective mass (similar to 2.3m(0)) of majority carriers (holes). Notably, charge carrier transport is found to be anisotropic, with hole mobilities being practically null in-plane and finite out-of-plane for these 2D COFs.