Considering the full dynamics of the different conversion stages from ocean waves to the electricity grid is essential to evaluate the realistic power flow in the drive train and design accurate model-based control formulations. The power take-off system for wave energy converters (WECs) is one of the essential parts of wave-to-wire (W2W) models, for which hydraulic transmissions are a robust solution and offer the flexibility to design specific drive-trains for specific energy absorption requirements of different WECs. The potential hydraulic drive train topologies can be classified into two main configuration groups (constant-pressure and variable-pressure configurations), each of which uses specific components and has a particular impact on the preceding and following stages of the drive train. The present paper describes the models for both configurations, including the main nonlinear dynamics, losses and constraints. Results from the mathematical model simulations are compared against experimental results obtained from two independent test rigs, which represent the two main configurations, and high-fidelity software. Special attention is paid to the impact of friction in the hydraulic cylinder and flow and torque losses in the hydraulic motor. Results demonstrate the effectiveness of the models in reproducing experimental results, capturing friction effects and showing similar losses.