Quantum machine learning has emerged as a promising application domain for near-term quantum hardware, particularly through hybrid quantum-classical models that leverage both classical and quantum processing. Although numerous hybrid architectures have been proposed and demonstrated successfully on benchmark tasks, a significant open question remains regarding the specific contribution of quantum components to the overall performance of these models. In this work, we aim to shed light on the impact of quantum processing within hybrid quantum-classical neural network architectures through a rigorous statistical study. We systematically assess common hybrid models on medical signal data as well as planar and volumetric images, examining the influence attributable to classical and quantum aspects such as encoding schemes, entanglement, and circuit size. We find that in best-case scenarios, hybrid models show performance comparable to their classical counterparts, however, in most cases, performance metrics deteriorate under the influence of quantum components. Our multi-modal analysis provides realistic insights into the contributions of quantum components and advocates for cautious claims and design choices for hybrid models in near-term applications.