Modern deep learning offers powerful tools for automated retinal screening, but it remains unclear how different visual model families compare in realistic multi-disease settings and under domain shift. In this work, we benchmark twelve architectures across four model families: convolutional neural networks, vision transformers, hybrid CNN-transformer backbones, and vision-language models, using the Retinal Fundus Multi-disease Image Dataset (RFMiD). We evaluate two tasks: binary screening for any retinal disease and multi-label classification across 28 disease classes. Using standardized training, calibration, and evaluation protocols, we report AUC, F1, precision, recall, and sensitivity at a clinically relevant operating point with specificity near 80%. On RFMiD, all architectures perform well on binary screening, with AUC above 84%, but attention-based models perform best. SwinTiny and the hybrid CoAtNet0 and MaxViTTiny models achieve the strongest binary screening results and improve macro and micro F1 in the multi-label setting. Vision-language models, including CLIP ViT-B/16 and SigLIP-Base384, are competitive with CNN baselines but do not surpass the best transformer and hybrid backbones. In external validation on Messidor-2 for referable diabetic retinopathy, AUC ranges from 66.8% to 84.7%, with hybrid and transformer models again showing strong performance. These results provide a reproducible reference for model selection in multi-disease retinal screening and guide future automated screening tools for clinical deployment.