In recent years, there has been interest in how geometric properties such as intrinsic dimension (ID) of a neural network's hidden representations change through its layers, and how such properties are predictive of important model behavior such as generalization ability. However, evidence has begun to emerge that such behavior can change significantly depending on the domain of the network's training data, such as natural versus medical images. Here, we further this inquiry by exploring how the ID of a network's learned representations changes through its layers, in essence, characterizing how the network successively refines the information content of input data to be used for predictions. Analyzing eleven natural and medical image datasets across six network architectures, we find that how ID changes through the network differs noticeably between natural and medical image models. Specifically, medical image models peak in representation ID earlier in the network, implying a difference in the image features and their abstractness that are typically used for downstream tasks in these domains. Additionally, we discover a strong correlation of this peak representation ID with the ID of the data in its input space, implying that the intrinsic information content of a model's learned representations is guided by that of the data it was trained on. Overall, our findings emphasize notable discrepancies in network behavior between natural and non-natural imaging domains regarding hidden representation information content, and provide further insights into how a network's learned features are shaped by its training data.