Building-integrated distributed energy storage offers a promising route toward energy self-sufficiency in buildings. In this study, industrial solid-waste-based composite structural electrodes were fabricated by incorporating graphene nanoplatelets (GNP) or carbon nanotubes (CNT) into cementitious matrices, and their effects on mechanical performance, electrochemical behavior, and hydration-induced conductive-network evolution were systematically compared. Both carbon materials markedly enhanced energy-storage performance but reduced compressive strength. GNP increased the areal capacitance by up to 1040-fold to 436.93 mF/cm², exceeding the 499-fold enhancement achieved by CNT, but caused a greater strength loss (64% vs. 46%). The superior capacitance of GNP was associated with its two-dimensional lamellar morphology, which provides a large electrochemically accessible surface and facilitates sheet-based electron transport. However, continued hydration progressively covered GNP surfaces and promoted agglomeration/restacking, leading to capacitance attenuation. In contrast, the fibrous morphology of CNT helped maintain conductive-network continuity across pore channels and hydration products, resulting in better electrochemical stability with curing age. A Structure–Energy Integrated Score (SEIS) based on compressive strength, areal capacitance, and the Warburg coefficient further showed that dosage optimization should balance energy-storage gains against load-bearing losses. These findings provide guidance for designing solid-waste-based structural energy-storage electrodes.