An apparatus in one embodiment comprises a storage system having a plurality of storage devices configured to store at least a first set of data. The storage system is configured to generate a first signature for the first set of data and to verify equivalence between the first set of data and a second set of data by comparing the first signature to a second signature generated for the second set of data. The first and second sets of data comprise respective first and second sets of pages with each page having a content-based page identifier and a page address, and the first and second signatures are generated as respective functions of the page identifiers and page addresses of the respective first and second sets of pages. The first and second sets of data may comprise respective first and second storage volumes, respective first and second sets of multiple storage volumes, or other sets of data.