A hybrid system integrating a power take-off (PTO) system into a floating breakwater is a promising candidate for both shoreline protection and commercial wave energy extraction. Although geometric asymmetry is important to such PTO-integrated breakwaters, its role in energy conversion efficiency and wave attenuation is poorly understood. In this study, a two-dimensional semi-analytical model dealing with floats with arbitrary bottom shapes is established based on the potential flow theory. To quantify the geometric asymmetry reflected by PTO-integrated breakwaters with different contours, the degree of asymmetry and the absolute asymmetry are newly defined mathematically. A set of symmetric and asymmetric PTO-integrated breakwaters are comparatively studied to demonstrate the effect of linear PTO damping and geometric asymmetry on the transmission coefficient, the reflection coefficient, and the energy conversion efficiency. Results show that no matter the hybrid system is symmetric or asymmetric, a larger PTO damping is beneficial for wave attenuation in longer waves, particularly at the heaving natural period of the device. On the premise that the PTO damping is optimized, an increase in the degree of asymmetry greatly improves the energy conversion efficiency. An increase in the absolute asymmetry slightly improves wave attenuation.