While the distinction between fuzzing and PBT is, er, fuzzy, what is unquestionable is that PBT is not meant to be coverage driven. It is a means to document behaviour for other developers in a way that is, in some cases, more descriptive than providing a fixed set of examples or other "traditional" ways of providing such documentation. Seeking coverage and "interesting" cases, rather than providing documentation, is decidedly the role of fuzzing.
Also: https://news.ycombinator.com/item?id=30385195
But, it occurs to me I could try and build on the same API, and compare them for effectiveness.