I noticed that PyPy does not show any real speed improvement over CPython in these benchmarks: https://www.techempower.com/benchmarks/
If you filter by Python, you can compare some results running on both CPython and PyPy. I would be curious to know what it is about these benchmarks that makes PyPy perform poorly. I would also be interested to see how Nuitka performs.
At the moment I'm also very excited about Pyston from Dropbox: https://github.com/dropbox/pyston
I'm supremely sceptical about those benchmarks. Go take a look at the code being tested. I would welcome a serious look at developmental time versus resource used, using code that is probable in production. I read the code used to test Django. It's not reasonable code.
It's an open sourced benchmarking comparison. If you can improve them, shoot them a pull request!