We have investigated pressure- and magnetic-field-dependent electrical transport properties in the charge transfer salts β-(BDA-TTP)2MCl4 (M=Fe,Ga), both of which show a metal-insulator (MI) transition around 120 K at ambient pressure. The zero field temperature-pressure phase diagrams of the two compounds are quite similar; the MI transition temperature decreases with pressure, and superconductivity is observed in both the magnetic and non-magnetic compounds above ∼4.5 kbar. Likewise, Shubnikov-de Haas effect measurements show nearly identical Fermi surfaces. These similarities suggest that the magnetic interaction J between the conduction electrons and the magnetic moments in β-(BDA-TTP)2FeCl4 is small. Nevertheless, magnetoresistance measurements show remarkable differences and reveal that magnetic interactions with the conduction electrons are still effective in M=Fe compounds.