This paper proposes a performance analysis of a medium-range airliner powered by liquid hydrogen (LH2) propulsion. The focus is on operating performance in terms of achievable payload and range. A non-conventional box-wing architecture was selected to maximize operating performance. An optimization-based multidisciplinary design framework was developed to retrofit a baseline medium-range box-wing aircraft by designing and integrating the fuel tanks needed to store the LH2; several solutions were investigated for tank arrangement and layout by means of sensitivity analyses. As a main outcome, a performance analysis of the proposed LH2-powered box-wing aircraft is provided, highlighting the impact of the introduction of this energy carrier (and the integration of the related tank systems) on aircraft operating performance; a comparative study with respect to a competitor LH2-retrofitted tube-and-wing aircraft is also provided, to highlight the main possible operating differences between the two architectures. The findings reveal that the retrofitted box-wing can achieve long-range flights at the cost of a substantially reduced payload, mainly due to the volume limitations imposed by the installation of LH2 tanks, or it can preserve payload capacity at the expense of a significant reduction in range, as the trade-off implies a reduction in on-board LH2 mass. Specifically, the studied box-wing configuration can achieve a range of 7100 km transporting 150 passengers, or shorter ranges of 2300 km transporting 230 passengers. The competitor LH2-retrofitted tube-and-wing aircraft, operating in the same category and compatible with the same airport apron constraints, could achieve a distance of 1500 km transporting 110 passengers.