Abstract. As the need to transition from global reliance on fossil fuels grows, solutions for producing green alternative fuels are necessary. These fuels will be especially important for hard-to-decarbonize sectors such as shipping. Mobile offshore wind energy systems (MOWESs) have been proposed as one such solution. These systems aim to harness the far-offshore wind resource, which is abundant and yet untapped because of installation and grid-connection limitations. Two classes of MOWES have been proposed in the literature: unmoored floating offshore wind turbines (UFOWTs) and energy ships (ESs). Both systems operate as autonomous Power to X (PtX) plants, powered entirely by wind energy, and so can be used to produce synthetic green fuels such as hydrogen or ammonia, or for other energy intensive applications such as direct air carbon capture. The two technologies differ in form; UFOWTs are based on a conventional FOWT but include propellers in place of mooring lines for sea-/course-keeping, while ESs operate like a sailing ship and generate power via hydroturbines mounted on the underside of the hull. Though much research and development is necessary for these systems to be feasible, the promise of harnessing strong winds far offshore, as well as the potential to avoid siting regulatory challenges, are enticing. This paper develops models of each MOWES concept to compare their power production on a consistent basis. The performance of the technologies are examined at steady-state operating points across relative wind speeds and angles. An optimization scheme is used to determine the values of the control variables which define the operating point for each set of environmental conditions. Results for each model show good agreement with published results for both UFOWTs and ESs. Model results suggest that UFOWTs can generate more power than ESs under ideal environmental conditions, but are very sensitive to off-design operating conditions. In above-rated wind speeds, the UFOWT is able to produce as much power as a conventional, moored FOWT, whereas the ES cannot, since some power is always consumed to spin the Flettner rotors. The models developed here and their results may both be useful in future works that focus on the routing of UFOWTs, or holistically designing a mobile UFOWT. Although differences in the performance of the systems have been identified, more work is necessary to discern which is a more viable producer of green e-fuels.