Material extrusion (MEX) of metallic powder-based filaments has shown great potential as an additive manufacturing (AM) technology. MEX provides an easy solution as an alternative to direct additive manufacturing technologies (e.g., Selective Laser Melting, Electron Beam Melting, Direct Energy Deposition) for problematic metallic powders such as copper, essential due to its reflectivity and thermal conductivity. MEX, an indirect AM technology, consists of five steps—optimisation of mixing of metal powder, binder, and additives (feedstock); filament production; shaping from strands; debinding; sintering. The great challenge in MEX is, undoubtedly, filament manufacturing for optimal green density, and consequently the best sintered properties. The filament, to be extrudable, must accomplish at optimal powder volume concentration (CPVC) with good rheological performance, flexibility, and stiffness. In this study, a feedstock composition (similar binder, additives, and CPVC; 61 vol. %) of copper powder with three different particle powder characteristics was selected in order to highlight their role in the final product. The quality of the filaments, strands, and 3D objects was analysed by micro-CT, highlighting the influence of the different powder characteristics on the homogeneity and defects of the greens; sintered quality was also analysed regarding microstructure and hardness. The filament based on particles powder with D50 close to 11 µm, and straight distribution of particles size showed the best homogeneity and the lowest defects.