Automatic image rotation estimation is a key preprocessing step in many vision pipelines. This task is challenging because angles have circular topology, creating boundary discontinuities that hinder standard regression methods. We present a comprehensive study of five circular-aware methods for global orientation estimation: direct angle regression with circular loss, classification via angular binning, unit-vector regression, phase-shifting coder, and circular Gaussian distribution. Using transfer learning from ImageNet-pretrained models, we systematically evaluate these methods across sixteen modern architectures by adapting their output heads for rotation-specific predictions. Our results show that probabilistic methods, particularly the circular Gaussian distribution, are the most robust across architectures, while classification achieves the best accuracy on well-matched backbones but suffers training instabilities on others. The best configuration (classification with EfficientViT-B3) achieves a mean absolute error (MAE) of 1.23° (mean across five independent runs) on the DRC-D dataset, while the circular Gaussian distribution with MambaOut Base achieves a virtually identical 1.24° with greater robustness across backbones. Training and evaluating our top-performing method-architecture combinations on COCO 2014, the best configuration reaches 3.71° MAE, improving substantially over prior work, with further improvement to 2.84° on the larger COCO 2017 dataset.