The increasing penetration of variable renewable energies poses new challenges for grid management. The economic feasibility of grid-balancing plants may be limited by low annual operating hours if they work either only for power generation or only for power storage. This issue might be addressed by a dual-function power plant with power-to-x capability, which can produce electricity or store excess renewable electricity into chemicals at different periods. Such a plant can be uniquely enabled by a solid-oxide cell stack, which can switch between fuel cell and electrolysis with the same stack. This paper investigates the optimal conceptual design of this type of plant, represented by power-to-x-to-power process chains with x being hydrogen, syngas, methane, methanol and ammonia, concerning the efficiency (on a lower heating value) and power densities. The results show that an increase in current density leads to an increased oxygen flow rate and a decreased reactant utilization at the stack level for its thermal management, and an increased power density and a decreased efficiency at the system level. The power-generation efficiency is ranked as methane (65.9%), methanol (60.2%), ammonia (58.2%), hydrogen (58.3%), syngas (53.3%) at 0.4 A/cm2, due to the benefit of heat-to-chemical-energy conversion by chemical reformulating and the deterioration of electrochemical performance by the dilution of hydrogen. The power-storage efficiency is ranked as syngas (80%), hydrogen (74%), methane (72%), methanol (68%), ammonia (66%) at 0.7 A/cm2, mainly due to the benefit of co-electrolysis and the chemical energy loss occurring in the chemical synthesis reactions. The lost chemical energy improves plant-wise heat integration and compensates for its adverse effect on power-storage efficiency. Combining these efficiency numbers of the two modes results in a rank of round-trip efficiency: methane (47.5%) > syngas (43.3%) ≈ hydrogen (42.6%) > methanol (40.7%) > ammonia (38.6%). The pool of plant designs obtained lays the basis for the optimal deployment of this balancing technology for specific applications.