Efficient and affordable electricity storage systems have a significant potential to support the growth and increasing penetration of intermittent renewable-energy generation into the grid from an energy system planning and management perspective, while differences in the demand and price of peak and off-peak electricity can make its storage of economic interest. Technical (e.g., roundtrip efficiency, energy and power capacity) as well as economic (e.g., capital, operating and maintenance costs) indicators are anticipated to have a significant combined impact on the competitiveness of any electricity storage technology or system under consideration and, ultimately, will crucially determine their uptake and implementation. In this paper, we present thermoeconomic models of two recently proposed medium- to large-scale electricity storage systems, namely 'Pumped-Thermal Electricity Storage' (PTES) and liquid-Air Energy Storage' (LAES), focusing on system efficiency and costs. The LAES thermodynamic model is validated against data from an operational pilot plant in the UK; no such equivalent PTES plant exists, although one is currently under construction. As common with most newly proposed technologies, the absence of cost data results to the economic analysis and comparison being a significant challenge. Therefore, a costing effort for the two electricity storage systems that includes multiple costing approaches based on the module costing technique is presented, with the overriding aim of conducting a preliminary economic feasibility assessment and comparison of the two systems. Based on the results, it appears that PTES has the potential to achieve higher roundtrip efficiencies, although this remains to be demonstrated. LAES performance is found to be significantly enhanced through the integration and utilisation of waste heat (and cold) streams. In terms of economics on the other hand, and at the system size intended for commercial application, LAES (12 MW, 50 MWh) is estimated in this work to have a lower capital cost and a lower levelised cost of storage than PTES (2 MW, 11.5 MWh), although it is noted that the prediction of the economic proposition of PTES technology is particularly uncertain if customised components are employed. However, when considering the required sell-to-buy price ratios, PTES appears (by a small margin) economically more competitive above an electricity buy price of similar to 0.15 $/kWh, primarily due to its higher roundtrip efficiency. When considering the two systems at the same capacity, the costs are similar with a slight edge to PTES. Finally, it is of interest that the most expensive components in both systems are the compression and expansion devices, which suggests that there is a need to develop affordable high-performance devices for such systems.