Here are a couple options you could consider to compare table contents instead of the ‘minus’ operator:
Oracle change tables are probably the best for tracking changes internal to the database. You can see an example of them here.
This is what most Oracle data warehouse ETL is built with.
Custom triggers on insert, update and delete can enable similar functionality to change tables (change tables actually work with internal triggers.) You can have the triggers insert your data into another table or just keep some metadata in a separate table to indicate which rows have changed.
Simply adding an activity date column to your tables, populated with a trigger may be enough to track changes and keep databases in sync. If you know, for example, that the database was cloned at midnight on the 1st of the month, then to see what has changed since then you just need to examine all rows with an activity date after that. The activity date can be useful for several other things as well making this a fairly desirable approach.
Blake has an intriguingly eclectic blog himself which is well worth a visit. Thanks for the question Blake!