The accurate interpretation of chest radiographs using automated methods is a critical task in medical imaging. This paper presents a comparative analysis between a supervised lightweight Convolutional Neural Network (CNN) and a state-of-the-art, zero-shot medical Vision-Language Model (VLM), BiomedCLIP, across two distinct diagnostic tasks: pneumonia detection on the PneumoniaMNIST benchmark and tuberculosis detection on the Shenzhen TB dataset. Our experiments show that supervised CNNs serve as highly competitive baselines in both cases. While the default zero-shot performance of the VLM is lower, we demonstrate that its potential can be unlocked via a simple yet crucial remedy: decision threshold calibration. By optimizing the classification threshold on a validation set, the performance of BiomedCLIP is significantly boosted across both datasets. For pneumonia detection, calibration enables the zero-shot VLM to achieve a superior F1-score of 0.8841, surpassing the supervised CNN's 0.8803. For tuberculosis detection, calibration dramatically improves the F1-score from 0.4812 to 0.7684, bringing it close to the supervised baseline's 0.7834. This work highlights a key insight: proper calibration is essential for leveraging the full diagnostic power of zero-shot VLMs, enabling them to match or even outperform efficient, task-specific supervised models.