In this study, quasi-static axial compression tests were conducted on mild steel bi-tubular architectures with rectangular nested tube (RNT) and square nested tube (SNT) geometries to evaluate their crushing and crashworthiness performance. A multi-criteria decision-making approach was employed to identify the optimal energy-absorbing architecture. The SNT structure, with the smallest gap size between the inner and outer tubes, exhibited the most desirable energy absorption characteristics among the considered cases. Acrylonitrile butadiene styrene (ABS) cores, with either rhombic or square cell configurations, were used to enhance the energy absorption performance of the SNT structure. A finite element model was created to evaluate the responses of the SNT structure filled with ABS cores. The validity of finite element simulations of the ABS cores and optimal architecture under axial compression were confirmed by comparing them with experimental results. The integration of the cores into the nested architecture enhanced crashworthiness performance and contributed to the control of the structure deformation. The SNT structure filled with rhombic ABS core exhibited superior crashworthiness performance compared to the counterpart filled with square core. The energy absorption of nested SNT structures filled with rhombic ABS core can be 116.93% greater than the corresponding non-filled structure. The crashworthiness indices of ABS-filled structures were highly sensitive to the number of cells and wall thickness of the core. A nested architecture with an ABS core could serve as a novel architecture for energy-absorbing devices.