Wave Power is one of the most investigated energy sources today. So far, several devices have been tested and built up to the pre-commercial stage. ISWEC (Inertial Sea Wave Energy Converter) has developed at the Politecnico di Torino, exploiting gyroscopes to extract wave energy. It allows power extraction without using any moving part immersed into water. The previous version of ISWEC presented 1 DOF (Degree Of Freedom), therefore requiring alignment of the device to the incoming wave; this paper describes a novel version of ISWEC, with 2 DOFs and consequently able to absorb power from every wave direction. The kinematics and the dynamics of the device are investigated, in order to compare the 1 DOF and the 2 DOF architectures from the point of view of the extracted power. The resulting simulations show that the 1 DOF prototype is more efficient when aligned with the incoming wave, while the behavior of the 2 DOF device is substantially independent of the wave direction. Such a difference of the performances is quantified and discussed along with considerations on the design and realization of the full-scale prototype.