Anisotropic magnetoelectric (ME) responses in bi-layered composites consisting of ferrites and polycrystalline/crystalline piezoelectrics were investigated by changing the applied DC magnetic field orientations, and origins for such effects were clarified by the competition between the dynamic piezomagnetic strain and the dynamic electro-mechanical strain from individual piezomagnetic/piezoelectric subsystems. Experimental results showed that maximum resonance ME voltage coefficient (MEVC) of 133.8.3 V/cm Oe under HDC = 23Oe can be obtained at θ = 0° for PMN-PT/NZFO laminate while one reached 115.3 V/cm Oe at higher field of 98Oe for θ = 75°. As rotation angle θ is varied from 0° to 360°, the HDC-orientation-dependent ME couplings were mainly determined by the dynamic piezomagnetic strain, and the dynamic piezoelectric coefficient versus θ profile can essentially track the MEVC versus θ profile. In addition, we found that the MEVC for PMN-PT/NZFO laminate is approximately twice as high as that of the PZT-8/NZFO laminate due to the stronger electro-mechanical strain of PMN-PT plates, Solid evidence was proved for the HDC-orientation-dependent ME coupling of the rectangle composite that is free of the influences of anisotropic crystalline orientation in PMN-PT plate. These findings open up a research pathway to move forward in this field and provide potential applications in vector angle sensors.