An apparatus in an illustrative embodiment comprises at least one processing device comprising a processor coupled to a memory. The processing device is configured to identify a storage volume to be migrated from a source storage system to a target storage system, and to issue one or more commands to at least one of the source storage system and a host device as part of a migration session for the storage volume. Responsive to the one or more commands, a plurality of data pages are received, with the data pages having respective hash values that are computed based at least in part on a native page size of the target storage system as specified in at least one of the one or more commands. The one or more commands illustratively comprise a plurality of read next page commands, with a given one of the read next page commands including information identifying the storage volume, the native page size of the target storage system, and the migration session.