Intervertebral cages made of Ti6Al4V alloy show excellent osteoconductivity, but also higher stiffness, compared to commonly used polyether-ether-ketone (PEEK) materials, that may lead to a stress-shielding effect and implant subsidence. In this study, a metallic intervertebral fusion cage, with improved mechanical behavior, was manufactured by the introduction of a three-dimensional (3D) mesh structure to Ti6Al4V material, using an additive manufacturing method. Then, the mechanical and biological properties of the following were compared: (1) PEEK, with a solid structure, (2) 3D-printed Ti6Al4V, with a solid structure, and (3) 3D-printed Ti6Al4V, with a mesh structure. A load-induced subsidence test demonstrated that the 3D-printed mesh Ti6Al4V cage had significantly lower tendency (by 15%) to subside compared to the PEEK implant. Biological assessment of the samples proved that all tested materials were biocompatible. However, both titanium samples (solid and mesh) were characterized by significantly higher bioactivity, osteoconductivity, and mineralization ability, compared to PEEK. Moreover, osteoblasts revealed stronger adhesion to the surface of the Ti6Al4V samples compared to PEEK material. Thus, it was clearly shown that the 3D-printed mesh Ti6Al4V cage possesses all the features for optimal spinal implant, since it carries low risk of implant subsidence and provides good osseointegration at the bone-implant interface.