Any metadata that you changed will have been changed in the library calibre was reading, which should be at C:\Users\Patrick\Calibre Library\
And Dropbox has a copy at C:\Users\Patrick\Dropbox\Calibre Library.
If you switch libraries to the one in dropbox, it will show the state of your library as it was when the copy was made. If you have added books, changed the titles, tags, authors, ids, anything whatsoever other than just clicking on books to read it or sending them to a device, you will have unsaved changes in the original library that do not appear in the dropbox library.
Perhaps I can illustrate with a
Mashal.
Imagine you have a word document. C:\Users\Patrick\My Documents\Book-list.docx. You edit it a lot, maybe ('cause it has a list of your books in it.) Then one day, you accidentally save a copy of this doc in Dropbox, at C:\Users\Patrick\Dropbox\Book-list.docx
You don't even realize this, of course. You continue using C:\Users\Patrick\My Documents\Book-list.docx with blithe assurance, notating a whole bunch of new books, books read, random thoughts of the day, whatever.
A while later you come upon C:\Users\Patrick\Dropbox\Book-list.docx and are like "hey, cool, why don't I use this instead?" But it is a little unreasonable to expect the changes to have been applied to the Dropboxed doc,
when it was never opened for editing!! The one in My Documents was the one edited!