Warning: a Cython core developer’s opinion ahead.
I almost always recommend Cython over ctypes. The reason is that it has a much smoother upgrade path. If you use ctypes, many things will be simple at first, and it’s certainly cool to write your FFI code in plain Python, without compilation, build dependencies and all that. However, at some point, you will almost certainly find that you have to call into your C library a lot, either in a loop or in a longer series of interdependent calls, and you would like to speed that up. That’s the point where you’ll notice that you can’t do that with ctypes. Or, when you need callback functions and you find that your Python callback code becomes a bottleneck, you’d like to speed it up and/or move it down into C as well. Again, you cannot do that with ctypes. So you have to switch languages at that point and start rewriting parts of your code, potentially reverse engineering your Python/ctypes code into plain C, thus spoiling the whole benefit of writing your code in plain Python in the first place.
With Cython, OTOH, you’re completely free to make the wrapping and calling code as thin or thick as you want. You can start with simple calls into your C code from regular Python code, and Cython will translate them into native C calls, without any additional calling overhead, and with an extremely low conversion overhead for Python parameters. When you notice that you need even more performance at some point where you are making too many expensive calls into your C library, you can start annotating your surrounding Python code with static types and let Cython optimise it straight down into C for you. Or, you can start rewriting parts of your C code in Cython in order to avoid calls and to specialise and tighten your loops algorithmically. And if you need a fast callback, just write a function with the appropriate signature and pass it into the C callback registry directly. Again, no overhead, and it gives you plain C calling performance. And in the much less likely case that you really cannot get your code fast enough in Cython, you can still consider rewriting the truly critical parts of it in C (or C++ or Fortran) and call it from your Cython code naturally and natively. But then, this really becomes the last resort instead of the only option.
So, ctypes is nice to do simple things and to quickly get something running. However, as soon as things start to grow, you’ll most likely come to the point where you notice that you’d better used Cython right from the start.