Reliable uncertainty quantification is crucial for trustworthy decision-making and the deployment of AI models in medical imaging. While prior work has explored the ability of neural networks to quantify predictive, epistemic, and aleatoric uncertainties using an information-theoretical approach in synthetic or well-defined data settings like natural image classification, its applicability to real-life medical diagnosis tasks remains underexplored. In this study, we provide an extensive uncertainty quantification benchmark for multi-label chest X-ray classification using the MIMIC-CXR-JPG dataset. We evaluate 13 uncertainty quantification methods for convolutional (ResNet) and transformer-based (Vision Transformer) architectures across a wide range of tasks. Additionally, we extend Evidential Deep Learning, HetClass NNs, and Deep Deterministic Uncertainty to the multi-label setting. Our analysis provides insights into uncertainty estimation effectiveness and the ability to disentangle epistemic and aleatoric uncertainties, revealing method- and architecture-specific strengths and limitations.