The environmental impact of emissions of fossil fuels and their rising prices, together with countries' commitment to mitigate the effect of the alarming and rapid climate changes, have been a crucial thrust to investigate new solutions to have an energy supply depending on renewable energies. In this scenario, offshore wind-wave hybrid platforms have been recently promoted: sharing facilities, infrastructure, and grid connections, give these systems the potential to increase energy production at a lower cost. However, an efficient realisation of these two combined technologies requires two potentially conflicting control objectives: On the one hand, for the wind turbine, a reduced movement of the platform is required, which essentially translates to enhanced stability of the structure, so that its behaviour resembles standard onshore wind technologies. On the other hand, to maximise the energy produced, wave energy converters (WECs) require optimal control technology, which often leads to large amplitude motion, potentially conflicting with the stability requirement for the wind turbine. The aim of this study is to investigate the effects of design changes on the dynamics of the hybrid wind-wave platform under energy-maximising control, which can be analysed in terms of the principle of impedance-matching. A semi-submersible platform with an incorporated flap-type WEC will be analysed both from a closed-loop and open-loop perspective, and the control system will be designed to maximise the energy produced by the WEC. Design changes on the wind-wave conversion platform will be in terms of flap dimensions, starting from a nominal geometry based on the so-called Oyster system. Analyses will be conducted by both increasing and decreasing the flap depth from the nominal case, to investigate the effect of the different geometries on the interactions between the WEC and the platform. A frequency-domain analysis of the overall input/output (velocity) system will be presented, highlighting the situations that can enhance the potential of both devices and exploit their synergies.