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Migration from CPython to PyPy is the last thing you should consider when thinking about web site performance (after architecture, database, caching, distributed queues, etc.). And if you absolutely need code-level optimizations (as shown by thorough profiling), then consider going straight to C/C++ for ultimate speed.
PyPy is mostly compatible with CPython on language and standard library level, but it’s incompatible with many CPython C extensions (and the compatible ones may actually work slower). If your site is pure Python and has proper test coverage, you can easily check if it works with PyPy and if it’s considerably faster or not. If you don’t have tests, things are getting risky. If you use C extensions, you’ll face issues and it’s likely more trouble than it’s worth.
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