Incorporating the non-ideal power take-off (PTO) efficiency of wave energy converters (WECs) into energy-maximizing control is crucial for achieving optimal electrical power generation. The majority of previous loss-aware controllers are based on a simplified power-coefficient (PC) model or only consider the copper loss, which remain insufficient to describe a real electrical PTO. In this article, a high-fidelity loss model, encompassing different loss components of the PTO (a generator and a power converter), is developed, and a number of loss-aware model predictive control (MPC) options are derived and compared in a realistic case study. The results highlight the importance of using an appropriate loss model, rather than a PC model, both for power evaluation and for control, and it is shown that a quadratic loss model employed in MPC is effective in approximating the true loss function, so that near-optimal power production can be achieved with fast computation.