Catherine the Great and Peter the Great had some significant character falws, I believe. I know the rules are different for royals and pontiffs, but what I mean is, "the Great" as a label needn't imply anything about being progressive or regressive or whatever.

I suppose if he did end up being called "John Paul the Great" rather than "John Paul the Second" it'd mean his predecessor being called "John Paul the Lesser", 33 days being a lot less than 26 years. It might be good if the new man could be someone on the lines of JP the First, to balance things out.