Satellite-derived bathymetry (SDB) has an extensive prospect in nearshore bathymetry for its high efficiency and low costs. Atmospheric correction and bathymetric modeling are critical processes in SDB, and examining the performance of related algorithms and models will contribute to the formulation of reliable bathymetry strategies. This study explored the effectiveness of three general atmospheric correction algorithms, namely Second Simulation of a Satellite Signal in the Solar Spectrum (6S), Atmospheric correction for OLI 'lite' (ACOLITE), and QUick Atmospheric Correction (QUAC), in depth retrieval from Landsat-8 and Sentinel-2A images using different SDB models over Ganquan Island and Oahu Island. The bathymetric Light Detection and Ranging (LiDAR) data was used for SDB model training and accuracy verification. The results indicated that the three atmospheric correction algorithms could provide effective corrections for SDB. For the SDB models except log-transformed band ratio model (LBR) and support vector machine (SVM), the impact of different atmospheric corrections on bathymetry was basically the same. Furthermore, we assessed the performance of six different SDB models: Lyzenga's model (LM), generalized additive model (GAM), LBR, SVM, multilayer perceptron (MLP), and random forest (RF). The bathymetric accuracy, consistency of bathymetric maps and generalization ability were considered for the assessment. Given sufficient training data, the accuracy of the machine learning models (SVM, MLP, RF) was generally superior to that of the empirical inversion models (LM, GAM, LBR), with the root mean square error (RMSE) varied between 0.735 m to 1.177 m. MLP achieved the best accuracy and consistency. When the depth was deeper than 15 m, the bathymetry error of all the SDB models increased sharply, and LM, LBR and SVM reached the upper limit of depth retrieval capability at 20-25 m. In addition, LM and LBR were demonstrated to have better adaptability in heterogeneous environment without training data.