Molecular spintronics is an effervescent field of research, which aims at combining spin physics and molecular nano-objects. In this article, we show that phthalocyanine molecules integrated in magnetic tunnel junctions (MTJs) can lead to magnetoresistance effects of different origins. We have investigated cobalt and manganese phthalocyanine molecule based magnetic tunnel junctions. CoPc MTJs exhibit both tunneling magnetoresistance (TMR) and tunneling anisotropic magnetoresistance (TAMR) effects of similar magnitude. However, for MnPc MTJs, a giant TAMR dominates with ratios up to ten thousands of percent. Strong features visible in the conductance suggest that spin-flip inelastic electron tunneling processes occur through the Mn atomic chain formed by the MnPc stacks. These results show that metallo-organic molecules could be used as a template to connect magnetic atomic chains or even a single magnetic atom in a solid-state device.