Polyurethane foams (PUF) are well-known materials in building construction. Innovative biobased polyurethane foams (BPUF) offer competitive alternatives to fossil-based formulations with the ongoing research driven by environmental and health concerns. In this paper, a comparison between an off-the-shelf fossil-based PUF and a custom-made BPUF was conducted. BPUF is based on a chemical formulation that replaces up to 70% of the main fossil-based reactants—polyol and isocyanate—with non-fossil alternatives. Both foams were embedded in the cavity of load-bearing composite masonry units as their insulation layer and binding agent. It was observed that while the density of fossil-based PUF inside the block completely changed from free-foamed declared values, the density of BPUF instead remained consistent to declared values. BPUF has also more (but smaller) number of pores than PUF detected by the microscope. Both types of foam samples were extracted from the block cavities and via dynamic scanning calorimetry (DSC) they were not undergoing any post-curing effects within the temperature working range of interest (10 °C−40 °C) hence they both perform at their best. The combination of such analyses with the results obtained from dynamic mechanical analyzer (DMA) shows that a carefully manufactured, custom-made mid density BPUF can outperform, in average, the mechanical properties of an all-purpose fossil-based PUF in both shear and tensile mode. The latter are stresses applied to the foam when the area of the block is either partially or fully loaded in compression mode. BPUF reached averages of E’ of 33.4 MPa (30 times higher than PUF) at 10 °C and 29.23 MPa (43.62 times over PUF) at 40 °C. In shear mode averages of G’ of 9.27 MPa (12.19 times higher than PUF) at 10 °C and 8.12 MPa (18.45 times higher than PUF) at 40 °C. Furthermore, both types of foam reached the lowest values of elastic modules in tensile and shear mode at their respective glass transition temperature measured by the DSC.