Objective quality assessment of stereoscopic 3D video is challenging but highly desirable, especially in the application of stereoscopic video compression and transmission, where useful quality models are missing, that can guide the critical decision making steps in the selection of mixed-resolution coding, asymmetric quantization, and pre- and post-processing schemes. Here we first carry out subjective quality assessment experiments on two databases that contain various asymmetrically compressed stereoscopic 3D videos obtained from mixed-resolution coding, asymmetric transform-domain quantization coding, their combinations, and the multiple choices of postprocessing techniques. We compare these asymmetric stereoscopic video coding schemes with symmetric coding methods and verify their potential coding gains. We observe a strong systematic bias when using direct averaging of 2D video quality of both views to predict 3D video quality. We then apply a binocular rivalry inspired model to account for the prediction bias, leading to a significantly improved full reference quality prediction model of stereoscopic videos. The model allows us to quantitatively predict the coding gain of different variations of asymmetric video compression, and provides new insight on the development of high efficiency 3D video coding schemes.