This study aims to compare the compression loads and stress transfer behavior in different core designs with stiff face sheets in sandwich composites. This study investigates the static axial compression behavior of three distinct cores: tubular square (conventional design), hexagonal tubes (bioinspired construction), and tetra chiral (auxetic design). The cores (square tubes, hexagonal tubes, and tetra chiral structures) were 3D printed using the fused deposition modeling (FDM) process with a polylactic acid (PLA) polymer filament. The experimental study showed that the compression loading behavior of all three cores transforms due to variations in stress transfer processes (by monitoring strain fields) identified using the digital image correlation (DIC) approach. Interestingly, square cores (unit cells with vertical walls) had the highest initial peak load, followed by tetra chiral and hexagonal cores. However, the sharp load drops in the square core structure (without a plateau regime) do not make this design suitable for commercial use. This sudden drop corresponds directly to the buckling of vertical cell walls. Overall, the preferred core design of a sandwich composite is tetra chiral (an auxetic structure), which demonstrated the highest peak load and energy absorption followed by a stable plastic regime with a stable and uniform stress transfer mechanism.