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Artificial intelligence (AI) can extract subtle visual information from digitized histopathology slides and yield scientific insight on genotype-phenotype interactions as well as clinically actionable recommendations. Classical weakly supervised pipelines use an end-to-end approach with residual neural networks (ResNets), modern convolutional neural networks such as EfficientNet, or non-convolutional architectures such as vision transformers (ViT). In addition, multiple-instance learning (MIL) and clustering-constrained attention MIL (CLAM) are being used for pathology image analysis. However, it is unclear how these different approaches perform relative to each other. Here, we implement and systematically compare all five methods in six clinically relevant end-to-end prediction tasks using data from N=4848 patients with rigorous external validation. We show that histological tumor subtyping of renal cell carcinoma is an easy task which approaches successfully solved with an area under the receiver operating curve (AUROC) of above 0.9 without any significant differences between approaches. In contrast, we report significant performance differences for mutation prediction in colorectal, gastric and bladder cancer. Weakly supervised ResNet-and ViT-based workflows significantly outperformed other methods, in particular MIL and CLAM for mutation prediction. As a reason for this higher performance we identify the ability of ResNet and ViT to assign high prediction scores to highly informative image regions with plausible histopathological image features. We make all source codes publicly available at https://github.com/KatherLab/HIA, allowing …