The mean-line method, as the corner stone of preliminary aerodynamic design of axial-flow compressors, is heavily dependent on the accuracy and robustness of empirical prediction models, mainly the deviation models and loss models. A large number of such models have been developed, however, a comprehensive evaluation of their prediction capabilities was lacked yet. To carry out the accuracy and sensitivity analysis of these prediction models developed in the both academic and industry communities, we here developed a one-dimensional mean-line method which implements several widely used deviation and loss models. Then, the developed mean-line method was applied to predict the speed-lines of aerodynamic performance for three representative transonic axial-flow compressors, i.e., NASA Rotor 35, NASA Stage 35 and NASA 74A first front three-stage. The parallel coordinates method was particularly adopted to effectively perform the sensitivity analysis of totally 2448 combinations of deviation and loss models through a heuristic comparison of the model predictions with the available experimental data. The accuracy analysis indicates that, by using the best model combinations, the prediction error of peak efficiency point is generally kept below 2% whereas that of surge margin varies significantly from 3.03% to 18.93%. However, the most accurate model combination is dependent on the compressor type and rotational speed. The sensitivity analysis shows that the prediction robustness is remarkably influenced by the deviation model accounting for axial velocity ratio effect, the design shock loss model and the off-design total loss model. This work provides the design engineers with prediction model selection, and the model developers with prediction improvement direction for axial-flow compressors.