Yes Delphix works with both, (check
here for Oracle version compatibility) however keep in mind: the big difference will be in the performance of the Snapshots. In standard edition of Oracle you don't have the capability of using a block change tracking file, so in order to take a snapshot, it has to read every block in a datafile versus looking up the changed blocks from the tracking file; this is an oracle limitation not a Delphix one.
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