With the increase of available protein-protein interaction (PPI) data, more and more efforts have been put to PPI network modeling, and a number of models of PPI networks have been proposed. Roughly speaking, good models of PPI networks should be able to accurately describe PPI mechanisms, and thus reproduce the structures of PPI networks. With such models, theoretical and/or computational biologists can efficiently explore the evolution and dynamics of PPI networks. However, a theoretical and/or computational biologist may feel confused when she/he has to choose a proper PPI model for her/his research work from a dozen of candidate models, while there is no guideline available to help her/him. To tackle this problem, in this article, we carry out a comprehensive performance comparison study on 12 existing models over PPI datasets of four species (yeast, mouse, fruit fly and nematode), by comparing the global and local statistical properties of the original PPI networks and the model-reproduced ones. To draw more convincing conclusions, we use the mean reciprocal rank to combine the ranks of a certain model on all statistical properties. Our experimental results indicate that the PS_Seed model [Solé and Pastor-Satorras (PS) model with seed] the STICKY model and the DD_Seed model (Duplication-Divergence model with seed) fit best with the test PPI datasets. By analyzing the underlying mechanisms of the models with better fitting ability, our analysis shows that the evolutionary mechanism of node duplication and link dynamics and the mechanisms with degree-weighted behaviors seem to be able to describe the PPI networks better.