The DisCoCirc framework for natural language processing allows the construction of compositional models of text, by combining units for individual words together according to the grammatical structure of the text. The compositional nature of a model can give rise to two things: compositional generalisation -- the ability of a model to generalise outside its training distribution by learning compositional rules underpinning the entire data distribution -- and compositional interpretability -- making sense of how the model works by inspecting its modular components in isolation, as well as the processes through which these components are combined. We present these notions in a framework-agnostic way using the language of category theory, and adapt a series of tests for compositional generalisation to this setting. Applying this to the DisCoCirc framework, we consider how well a selection of models can learn to compositionally generalise. We compare both quantum circuit based models, as well as classical neural networks, on a dataset derived from one of the bAbI tasks, extended to test a series of aspects of compositionality. Both architectures score within 5% of one another on the productivity and substitutivity tasks, but differ by at least 10% for the systematicity task, and exhibit different trends on the overgeneralisation tasks. Overall, we find the neural models are more prone to overfitting the Train data. Additionally, we demonstrate how to interpret a compositional model on one of the trained models. By considering how the model components interact with one another, we explain how the model behaves.