Offshore wind turbines (OWTs) play a critical role in renewable energy, requiring efficient methods to predict fatigue loads on their support structures under harsh environmental conditions. Traditional fatigue assessment methods are effective but costly and impractical at scale. Surrogate models (SMs) offer a cost-effective alternative, but site-specific SMs often fail to generalize across turbines in varying environments and locations. This study explores whether platform-generic SMs trained on a Simulation Database can serve as reliable replacements for site-specific SMs trained on Supervisory Control and Data Acquisition (SCADA) and Structural Health Monitoring (SHM) data for predicting fatigue loads in OWT support structures. The SMs, developed using both deterministic and Bayesian neural networks (NNs), were evaluated in three progressively complex model setups featuring SCADA signals, nacelle accelerations, and tower top strain gauges. Results showed that site-specific SMs generally achieved lower mean average percentage error (MAPE), with deterministic NNs at 47.1m lowest astronomical tide (LAT) in the fore-aft (FA) direction reducing errors from 16.8% to 7.2% and in the side-side (SS) direction from 27.0% to 4.5% as additional signals were introduced. Platform-generic SMs exhibited higher MAPEs due to the broader scope of the model and slight mismatches between simulated and real turbine dynamics, especially in the FA direction. Nonetheless, in the SS direction at 47.1m LAT, platform-generic SMs showed promising performance, achieving errors as low as 7.5% in one configuration. Although Bayesian NNs did not consistently lower errors compared with deterministic approaches, they provided valuable insights into how far test data deviated from the training distribution, helping identify the potential limits of the model. This capability has significant practical implications, as it can potentially serve as a tool for detecting sensor malfunctions or identifying irregular data, ensuring more reliable predictions in real-world applications. Overall, platform-generic SMs still require refinement before they can fully replace site-specific SMs, and Bayesian NNs should not replace deterministic NNs but rather serve as a valuable supplement.