In most studies applying deep learning to medical image analysis, classification accuracy is the sole optimization criterion, while the computational cost of the resulting models remains undocumented: parameter and operation counts are reported only occasionally, and inference latency on a central processing unit is almost never published. This makes an informed model choice impossible for institutions without graphics accelerators, such as district hospitals, mobile diagnostic units and field hospitals. This paper experimentally investigates the trade-off between diagnostic performance and computational resources for four-class chest X-ray classification. The computational cost of 15 widely used architectures was evaluated with a single tool at an input resolution of 224×224, and the gap between the heaviest and the lightest architecture reaches a factor of 323. Four models – a heavy baseline, two lightweight architectures, and a custom compact network – were trained under a unified protocol on the COVID-19 Radiography Database (21,165 images across four classes) and profiled strictly on a CPU with a batch size of one. The three standard architectures were initialized with ImageNet-pretrained weights, and the custom network was trained from scratch. Each architecture was trained across three independent random seeds on a fixed data split, so all performance metrics are reported as mean ± std, and every comparison is accompanied by a confidence interval and a significance test. The lightweight architecture trailed the baseline by only 1.24 percentage points in macro-F1 (95% CI: 0.84 to 1.63, p = 0.005) while requiring 69 times fewer operations, achieving 19.3 times lower latency, and reducing model size by a factor of 15.4; the efficiency metric, defined as macro-F1 per GFLOP, differs by a factor of 68. Additionally, post-training quantization systematically failed across all three runs for both architectures combining depthwise convolutions with Squeeze-and-Excitation blocks, whereas the same pipeline quantized the remaining models without statistically significant loss. Neither depthwise convolutions nor the Hard-Swish activation accounted for the failure; instead, the number of channel-wise multiplication nodes in the exported graph separated the two groups exactly, making the risk identifiable directly from the static graph prior to training. The practical implication is that the quantizability of a lightweight model must not be assumed; it must be verified empirically.