The situation you want to avoid is this:
Run tests, find bug.
Try and fix bug.
Rerun tests, tests pass.
Deploy fixes to production.
Later find out that the bug is not fixed, your second run of tests simply didn't hit the right combination.
Truth is, there's no need for an either/or holy war about this. The two styles are easily mixable: property based testing for broad coverage, specific runs for specific coverage.
Rather, to me, the issue is exhaustive testing vs. non-exhaustive testing. Typically, critical issues in complex systems only arise extremely rarely. Consequently, randomized testing typically does not bring them to light. There may definitely be cases where it is useful, and it can certainly easily be more exhaustive than a small hand-picked set of unit tests. But the core issue is still that I typically need exhaustive tests to be more certain about relevant properties.
All determinism guarantees is that you'll either reliably detect a bug or reliably not detect a bug, and hence get a nice aesthetic line of green checkmarks followed by red crosses in your test history. Or just get a nice looking line of green and not even know the bug is there. This seems like a small thing to sacrifice to detect more bugs.
Of course, regular unit tests have their place too, when your specification can't really be expressed as a "forall" property.