Structural Health Monitoring (SHM) is crucial for maintaining the sustainability and safety of civil infrastructure. The Z24 Bridge in Switzerland remains one of the benchmark datasets used to validate vibration-based damage detection methods. Traditional approaches based exclusively on modal parameters are frequently limited by data scarcity and environmental variability. Recent advances in artificial intelligence have enabled data-driven neural networks to learn discriminative features directly from raw measurements. Meanwhile, hybrid methods such as Physics-Informed Neural Networks (PINNs) incorporate governing physical laws into the learning process. This study presents a comparative analysis of three successive artificial Neural Network models (NN V1–V3) and One Physics-Informed Neural Network (PINN V1), all applied to the Z24 Bridge dataset. The NN models progressively improve in depth, optimization strategy, and regularization, achieving ≈97.7% validation accuracy and a macro AUC ≈1.00 with NN V3. However, they remain completely dependent on the quality and quantity of training data. In contrast, the PINN incorporates the differential equation of a damped oscillator into its loss function, balancing a data-driven term with a physics-based residual. This approach enables more stable learning with limited labeled data and ensures consistency with structural dynamics. Experimental results highlight the trade-off between accuracy and robustness: while NN V3 yields the highest predictive performance (≈97.7% validation accuracy, macro AUC ≈1.00), PINN V1 achieves slightly lower accuracy (≈92%) but offers improved stability and interpretability. This dual perspective demonstrates that hybrid physics-informed models provide a more reliable basis for decision-making in SHM. The findings underscore the potential of combining machine learning with physical knowledge, paving the way for future developments such as hybrid PINNs (HPINNs), multi-sensor integration, and high-performance computing deployment.