I want to extend python and numpy by writing some modules in C or C++, using BLAS and LAPACK. I also want to be able to distribute the code as standalone C/C++ libraries. I
First, there is one point in your question I don't get:
[...] also want to be able to distribute the code as standalone C/C++ libraries. [...] Some functions will need to call a Python function from the C/C++ code.
How is this supposed to work?
Next, as to your actual question, there are certainly advantages of using the Python/C API directly:
Most likely, you are more familar with writing C code than writing Cython code.
Writing your code in C gives you maximum control. To get the same performance from Cython code as from equivalent C code, you'll have to be very careful. You'll not only need to make sure to declare the types of all variables, you'll also have to set some flags adequately -- just one example is bounds checking. You will need intimate knowledge how Cython is working to get the best performance.
Cython code depends on Python. It does not seem to be a good idea to write code that should also be distributed as standalone C library in Cython