Developing robust artificial intelligence (AI) models that generalize well to unseen datasets is challenging and usually requires large and variable datasets, preferably from multiple institutions. In federated learning (FL), a model is trained collaboratively at numerous sites that hold local datasets without exchanging them. So far, the impact of training strategy, i.e., local versus collaborative, on the diagnostic on-domain and off-domain performance of AI models interpreting chest radiographs has not been assessed. Consequently, using 610,000 chest radiographs from five institutions across the globe, we assessed diagnostic performance as a function of training strategy (i.e., local vs. collaborative), network architecture (i.e., convolutional vs. transformer-based), generalization performance (i.e., on-domain vs. off-domain), imaging finding (i.e., cardiomegaly, pleural effusion, pneumonia, atelectasis, consolidation, pneumothorax, and no abnormality), dataset size (i.e., from n=18,000 to 213,921 radiographs), and dataset diversity. Large datasets not only showed minimal performance gains with FL but, in some instances, even exhibited decreases. In contrast, smaller datasets revealed marked improvements. Thus, on-domain performance was mainly driven by training data size. However, off-domain performance leaned more on training diversity. When trained collaboratively across diverse external institutions, AI models consistently surpassed models trained locally for off-domain tasks, emphasizing FL's potential in leveraging data diversity. In conclusion, FL can bolster diagnostic privacy, reproducibility, and off-domain reliability of AI models and, potentially, optimize healthcare outcomes.