Plastic User Interfaces (UIs) have the capacity to adapt to changes in their context of use while preserving usability. This exposes users to different versions of UIs that can diverge from each other at several levels, which may cause loss of consistency. This raises the question of similarity between UIs. This paper proposes an approach to comparing UIs by measuring to what extent UIs have the same interaction capabilities and appearance. We use the equivalence checking formal method. The approach verifies whether two UI models are equivalent or not. When they are not equivalent, the UI divergences are listed, thus providing the possibility of leaving them out of the analysis. In this case, the two UIs are said equivalent modulo such divergences. Furthermore, the approach shows that one UI can contain at least all interaction capabilities of another. We apply the approach to a case study in the nuclear power plant domain in which several UI versions are analyzed, and the equivalence and inclusion relations are demonstrated.