The equivalence class of the utility function should be the set of monotonous function of a canonical element.

However, what von Neumann-Morgenstern shows under mild assumptions is that for each class of utility functions, there is a subset of utility functions generated by the affine transforms of a single canonical element for which you can make decisions by computing expected utility. Therefore, looking at the set of all affine transforms of such an utility function really is the same as looking at the whole class. Still, it doesn't make utility commensurable.