Thanks for your question! The Doc-to-Doc Comparison tool was added to the Similarity Check service at the request of our users a few years ago. As you mention, it’s a way to compare one document against, up to five, others. Obviously, you could use this in both ways that you mention (comparing against versions of itself or against other docs that seem to have a similar subject), but I think the main reason our users were so interested in this feature is that it provides a way to compare a document against another document (or 5), without those other documents having to have been indexed by Turnitin or included in their database.
I would venture to guess that users find it the most useful when they have several manuscripts submitted at once on a particular subject. This feature allows you to compare them early on in the submission process, before DOIs are even registered and before they are published. The advantage is that you are comparing private documents at this stage.
If you do use this to compare versions of the same paper in order to see changes, do remember that this does count as a single document submission, so it will count towards your total of per-document checking fees.
I hope that helps answer your question! Please let me know if there’s anything else I can help with.