State space models (Mamba) have been proposed as a linear-complexity alternative to attention-based architectures, whose complexity is quadratic, but it remains unclear whether Mamba models outperform other linear-complexity networks, such as convolutional neural networks (CNNs), in image classification, an area relevant to medical imaging, where diagnostic accuracy and computational efficiency determine clinical viability. Extending a prior architectural analysis of the Cross-Scan routing mechanism, six ImageNet-pretrained architectures were trained, paired by size—three CNNs (ResNet-18, ResNet-50, EfficientNet-B0) and three Mamba models (Vim-S, VMamba-T, EfficientVMamba-S)—under an identical fairness-by-construction protocol (same preprocessing, optimizer, and training schedule). Protocol functionality was validated on Imagenette, and clinical validation was performed on ISIC-DICM-17K, a balanced binary (malignant/benign) dermoscopic dataset. Predictive performance was measured by assessing balanced accuracy, MCC, and AUROC, alongside computational efficiency in bfloat16 based on throughput, latency, VRAM consumption, resolution scaling, and the effective receptive field (ERF). VMamba-T, the hierarchical Mamba model, achieved the best performance in clinical validation, narrowly ahead of the best CNN, EfficientNet-B0. However, CNNs dominated efficiency: ResNet-50 reached 2.9 times the throughput of VMamba-T. VMamba-T's ERF was also markedly more global (edge-to-center ratio of 0.97) than ResNet-50's (0.74), explaining its accuracy advantage. No model dominated both axes in the Pareto analysis. Under matched conditions, Mamba does not universally outperform CNNs: each family occupies a distinct point on the accuracy–efficiency frontier, since Mamba's global-context advantage is offset by the youth of its architecture and the limited optimization of its kernels.