Not versed enough in Python and asyncio to replicate or understand his benchmark, however from my simplistic view async (or any concurrent framework really) should almost always be faster with any modern kind of application.
Let me give an example: If you run a web-service, chances are that you're gonna make some network call as part of processing a request, be it database, network, search index, etc. With async, these calls free up your application to work on another requests until the call returns. I'd say that many modern web-services are just a stitching-together of external calls (get-user-info-from-db, retrieve-user-items-from-db), so the only real work left for the web application to handle is to wait and parse/encode some JSON to client. If you can't max out your bandwidth in terms of JSON performance with one core you just start as many async processes as you have cores. The big advantage over sync processes then is that your async process can also handle insanely-long-running background calls while still crunching through the other requests. Someone please explain to me if I'm missing something here.