The simplest comparison related to bookmarks is to compare the number of bookmarks in two documents:

@Test
public void haveSameNumberOfBookmarks() throws Exception {
  String filenameTest = "documentUnderTest.pdf";
  String filenameReference = "reference.pdf";
  
  AssertThat.document(filenameTest)
            .and(filenameReference) 
            .haveSameNumberOfBookmarks()
  ;
}

Next, the bookmarks and their properties are compared. Bookmarks of two PDF documents are 'equal' if the following attributes have the same values:

@Test
public void haveSameBookmarks() throws Exception {
  String filenameTest = "documentUnderTest.pdf";
  String filenameReference = "reference.pdf";
  
  AssertThat.document(filenameTest)
            .and(filenameReference) 
            .haveSameBookmarks()
  ;
}

If you are uncertain about the bookmarks, all bookmark data can be extracted into an XML file using the utility ExtractBookmarks. This file can easily be analyzed. See chapter 9.5: “Extract Bookmarks to XML”.