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Underwater sound propagation is primarily driven by a nonlinear forward model relating variability of the ocean sound speed profile (SSP) to the acoustic observations (e.g., eigenray arrival times). Ocean acoustic tomography (OAT) methods aim at reconstructing SSP variations (with respect to a reference environment) from changes of the acoustic measurements between multiple source-receiver pairs. This article investigates the performance of three different OAT methods: (1) model-based methods (i.e., classical ray-based OAT using a linearized forward model), (2) data-driven methods (such as deep learning) to directly learn the inverse model, and (3) a hybrid solution [i.e., the neural adjoint (NA) method], which combines deep learning of the forward model with a standard recursive optimization to estimate SSPs. Additionally, synthetic SSPs were generated to augment the variability of the training set. These methods were tested with modeled ray arrivals calculated for a downward refracting environment with mild fluctuations of the thermocline. Idealized towed and fixed source configurations are considered. Results indicate that merging data-driven and model-based methods can benefit OAT predictions depending on the selected sensing configurations and actual ray coverage of the water column. But ultimately, the robustness of OAT predictions depends on the dynamics of the SSP variations. [ABSTRACT FROM AUTHOR]