Renewable sources of interest for the development of Hydraulic Converters are wave and wind energy. In both areas of application, the size of the installed machine is growing. This means handling more torque at the crankshaft, approaching the limit for electromechanical components available in series production. The hydraulic PTO stands out as an answer to the problem, being able to convert high torques at low speeds into low torques at high speeds, through robust and well-known systems and components. Alongside a review of the state of the art of hydraulic PTOs and the main control strategies applicable to wave energy extraction systems, the present work applies a hydraulic PTO to the ISWEC, an Inertial Sea Wave Energy Converter designed for the Adriatic Sea. When designing such hydraulic PTOs, it is necessary to consider components and control methods allowing control of the force - torque applied by the PTO to the prime mover and guaranteeing a constant generator speed. Sub-optimal configuration can result in very inefficient energy conversion, so understanding the design trade-offs is key to the success of the technology. Numerical analyses of a wave to wire time domain model are performed to compare the performances of two different hydraulic circuit configurations, both aiming to optimize the power production of the wave energy converter (WEC) considered.