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Privacy concerns around sharing personally identifiable information are a major barrier to data sharing in medical research. In many cases, researchers have no interest in a particular individual’s information but rather aim to derive insights at the level of cohorts. Here, we utilise generative adversarial networks (GANs) to create medical imaging datasets consisting entirely of synthetic patient data. The synthetic images ideally have, in aggregate, similar statistical properties to those of a source dataset but do not contain sensitive personal information. We assess the quality of synthetic data generated by two GAN models for chest radiographs with 14 radiology findings and brain computed tomography (CT) scans with six types of intracranial haemorrhages. We measure the synthetic image quality by the performance difference of predictive models trained on either the synthetic or the real dataset. We find that synthetic data performance disproportionately benefits from a reduced number of classes. Our benchmark also indicates that at low numbers of samples per class, label overfitting effects start to dominate GAN training. We conducted a reader study in which trained radiologists discriminate between synthetic and real images. In accordance with our benchmark results, the classification accuracy of radiologists improves with an increasing resolution. Our study offers valuable guidelines and outlines practical conditions under which insights derived from synthetic images are similar to those that would have been derived from real data. Our results indicate that synthetic data sharing may be an attractive alternative to sharing real patient-level data in the right setting.