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Determining whether two sets of images belong to the same or different domain is a crucial task in modern medical image analysis and deep learning, where domain shift is a common problem that commonly results in decreased model performance. This determination is also important to evaluate the output quality of generative models, e.g., image-to-image translation models used to mitigate domain shift. Current metrics for this either rely on the (potentially biased) choice of some downstream task such as segmentation, or adopt task-independent perceptual metrics (e.g., FID) from natural imaging which insufficiently capture anatomical consistency and realism in medical images. We introduce a new perceptual metric tailored for medical images: Radiomic Feature Distance (RaD), which utilizes standardized, clinically meaningful and interpretable image features. We show that RaD is superior to other metrics for out-of-domain (OOD) detection in a variety of experiments. Furthermore, RaD outperforms previous perceptual metrics (FID, KID, etc.) for image-to-image translation by correlating more strongly with downstream task performance as well as anatomical consistency and realism, and shows similar utility for evaluating unconditional image generation. RaD also offers additional benefits such as interpretability, as well as stability and computational efficiency at low sample sizes. Our results are supported by broad experiments spanning four multi-domain medical image datasets, nine downstream tasks, six image translation models, and other factors, highlighting the broad potential of RaD for medical image analysis.