It would be great to see a repo with this set of examples with code for both what is run under PyPy and the type-annotated cython code, and the exact settings that were used.
I run stuff I found in the cython repo only (good or bad) benchmarks/ or so. It was also ages ago so treat it with a grain of salt. My point is that there is no fundamental reason why cython should be faster than pypy (even with type annotations), because type annotations are essentially done during JITting. In fact, pypy should be faster because of other things, like a faster GC or objects.