Climate changes are increasingly impacting human welfare and, together with population growth, are rising the energy demand. To mitigate their negative effects, the need to harvest energy from renewable sources, while reducing the dependency on fossil fuels, has become pressing. This has led to the pursuit of new concepts that can exploit natural resources efficiently. In this scenario, offshore wind-wave hybrid platforms have been recently promoted: sharing facilities, infrastructure, and grid connections, gives 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 motion 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 required for the wind turbine. The aim of this study is to provide a better understanding of how the energy-maximising control problem for WEC systems interacts with both conversion systems, and to elucidate their corresponding synergies. A semi-submersible platform with an incorporated flap-type WEC is analysed from a closed-loop perspective, with the control system designed to maximise the energy produced by the WEC.