This article explores wood-fiber-based fabrics containing Lyocell yarn in the warp and Spinnova–Lyocell (60%/40%) yarn in the weft, which are used to form unidirectional all-cellulose composites (ACC) through partial dilution in a NaOH–urea solution. The aim is to investigate the role of the yarn orientation in composites, which was conducted by measuring the tensile properties in both the 0° and 90° directions. As a reference, thermoplastic biocomposites were prepared from the same fabrics, with biobased polypropylene (PP) as the matrix. We also compared the mechanical and thermal properties of the ACC and PP biocomposites. The following experiments were carried out: tensile test, TGA, DSC, DMA, water absorption test and SEM. The study found no significant difference in tensile strength regarding the Spinnova–Lyocell orientation between ACC and PP biocomposites, while the composite tensile strength was clearly higher in the warp (Lyocell) direction for both composite variants. Elongation at break doubled in ACC in the Lyocell direction compared with the other samples. Thermal analysis showed that mass reduction started at a lower temperature for ACC, but the thermal stability was higher compared with the PP biocomposites. Maximum thermal degradation temperature was measured as being 352 °C for ACC and 466 °C for neat PP, and the PP biocomposites had two peaks in the same temperature range (340–474 °C) as ACC and neat PP combined. ACCs absorbed 93% of their own dry weight in water in just one hour, whereas the PP biocomposites BC2 and BC4 absorbed only 10% and 6%, respectively. The study highlights the different properties of ACC and PP reference biocomposites that could lead to further development and research of commercial applications for ACC.