I think there's considerable overlap between classes of bugs that could be caught by static type checking and those that could be caught by unit tests. That said, I view the two as complementary and use both extensively.

One particularly interesting (though in my experience, rare) class of bugs are typing errors _in unit tests_. For example, an API under test expects one thing and a unit test supplies something else. If the test passes, it's hard to spot the problem without static type checking.