Pumped-thermal electricity storage (PTES), with the advantages of reduced geographical constraints, low capital costs, long lifetimes and flexible power ratings, is a promising large-scale energy storage technology for future power systems. In this work, thermo-economic models of Joule-Brayton PTES systems with solid thermal reservoirs (STRs) and liquid thermal stores (LTSs) were developed, and detailed parametric analyses of the two systems were performed. The results reveal that elevated maximum charging temperatures are beneficial for both thermodynamic and economic performance, and that there are optimal values for the packed-bed void fraction, heat-exchanger effectiveness and turbomachine polytropic pack from a thermo-economic perspective for the two PTES system variants. Multi-objective thermo-economic optimisation of PTES systems at a fixed power capacity (10 MW) and discharging duration (6 h) was also conducted. It is found that helium is the best working fluid candidate for both PTES systems, and that the best options for the storage material are magnetite for PTES systems with STRs, and the combination of Hitec XL + Therminol 66 + Butane for PTES systems with LTSs. In the investigated design space for both systems, PTES systems with STRs are more attractive as the total purchase cost is lower for the same roundtrip efficiency as PTES systems with LTSs. Using the technique for order of preference by similarity to the ideal solution decision-making method, and a selected weighted matrix (1:1), the optimal solutions amongst the Pareto front solutions were determined. The optimal roundtrip efficiency and total purchase cost are 71.8 % and 37.7 M$ for PTES systems with STRs, and are 56.0 % and 36.0 M$ for PTES systems with LTSs, respectively. The conclusions and proposed approach can provide useful guidance for the further development, design and optimisation of PTES technology.