You should definitely extract the data from the XML. Whether to extract it into a SQL vs a NoSQL DB is a different choice. You're likely to want a DB regardless, for the sake of the efficiency you get from indexing (compared to XML) even with a document store, and the flexibility you get from databases rather than custom native classes and data structures (though you may also want to build those on top of the DB layer).
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You should definitely extract the data from the XML. Whether to extract it into a SQL vs a NoSQL DB is a different choice. You're likely to want a DB regardless, for the sake of the efficiency you get from indexing (compared to XML) even with a document store, and the flexibility you get from databases rather than custom native classes and data structures (though you may also want to build those on top of the DB layer).