In this study, the effects of three processing stages: filament extrusion, 3D printing (FDM), and hot-pressing are investigated on electrical conductivity and tensile mechanical properties of poly(lactic) acid (PLA) composites filled with 6 wt.% of multiwall carbon nanotubes(MWCNTs), graphene nanoplatelets (GNPs), and combined fillers. The filaments show several decades’ higher electrical conductivity and 50–150% higher values of tensile characteristics, compared to the 3D printed and the hot-pressed samples due to the preferential orientation of nanoparticles during filament extrusion. Similar tensile properties and slightly higher electrical conductivity are found for the hot-pressed compared to the 3D printed samples, due to the reduction of interparticle distances, and consequently, the reduced tunneling resistances in the percolated network by hot pressing. Three structural types are observed in nanocomposite filaments depending on the distribution and interactions of fillers, such as segregated network, homogeneous network, and aggregated structure. The type of structural organization of MWCNTs, GNPs, and combined fillers in the matrix polymer is found determinant for the electrical and tensile properties. The crystallinity of the 3D printed samples is higher compared to the filament and hot-pressed samples, but this structural feature has a slight effect on the electrical and tensile properties. The results help in understanding the influence of processing on the properties of the final products based on PLA composites.