Diabetic retinopathy (DR) diagnosis delays pose a critical challenge for public healthcare systems such as the Brazilian Unified Health System (SUS), where long referral queues often prevent timely treatment and increase the risk of vision loss. Deep learning (DL) models offer an effective solution by automating retinal image analysis, but choosing an appropriate model requires balancing diagnostic accuracy with computational and energy efficiency. This study evaluates 38 convolutional neural networks (CNN) across four key dimensions: Area under the curve (AUC), energy consumption, model size, and training time. Our analysis identifies MobileNet as the superior architecture, demonstrating 77% lower energy use, 83% faster training, and 85% smaller model size than the InceptionV3 baseline, while achieving 3% higher AUC. We further optimize MobileNet through systematic hyperparameter tuning and evaluate its scalability on the ARM-based NVIDIA Grace Superchip, revealing peak efficiency at 36-thread configurations where energy use, CPU utilization, and memory access patterns reach optimal balance. All implementation scripts are publicly available to foster reproducible, sustainable AI development for clinical applications.