There are advantages with both. It is worth starting by stating that a research education is not about writing papers but to educate a person to become a self-reliant researcher. The thesis or dissertation is the document that shows the result of this effort.
From the perspective of showing the result of the education as such, the monograph probably better reflects the work done since articles normally brush away methods and other aspects through referencing. Articles often focus on a core piece of data and have no space for additional data that may have been collected. or shows data in a very condensed way. In a monographs much of this can be expanded upon and more of what was actually achieved during the study can be documented thoroughly. I occasionally bump into monographs that ha excellent detailed descriptions of methods or other aspects where I can really learn something new in a good way. This is of course not why anyone should write a monograph but the monograph can be an appreciated publication.
So the monograph provides possibilities for the PhD candidate to show the knowledge gained in a detailed way.
The cumulative thesis can probably also have different looks. In Scandinavia, the thesis consists of about 3-5 papers at different stages of completion (a basic rule is that they should be at least in shape to be sent in for peer review in a journal). Most students end up with a couple of published papers and a couple of manuscripts in their thesis. There is also a cover paper to be written where the different papers are shown in a larger perspective and which should tie the thesis together.
The benefit of this format is that the PhD candidate has publications under the belt by the time he/she finishes. This can also be true for anyone writing a monographs but then that person has to write on two things in parallel although much of it is likely a matter of reformatting. But the focus on papers is, regardless of how one feels about it, a necessity since almost everything that concerns evaluation in academia involves counting number of publications. So the more publications the better, basically. Doing a cumulative thesis is thus a more direct way into the "after-life" of scientific publishing.
Another point to bring up is the actual writing of a monograph. Since the monograph is a single entity the author has full control over the progress (bar intervention by the advisor) which makes it easier to complete with a set deadline. With a cumulative thesis, focus is on manuscripts which often involves more or less responding co-authors which in the end can complicate things and most importantly make deadlines more difficult to assess.
One should, however, not forget that it is possible to combine these to some extent. The cover paper for a cumulative thesis can probably look quite differently in different countries (academic cultures). There is, however, nothing that says that the cover paper could not contain just the parts I described are more or less unique to the monograph. This would then provide the best of both worlds.