There is no way to compare libraries using calibre itself, though you could do it using various other tools/approaches - for instance generate a csv catalog from both libraries, and then use a difference tool to tell you what is in one library on not the other based on the csv files.
As for keeping stuff in sync in future - you can use the Copy to Library function (it is on the right-click menu) to copy books from one library to another, including all their metadata (assuming the libraries are accessible from the same PC).
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