Most people understand that async Python has a higher level of concurrency. It would make some sense for that to imply higher performance for common tasks like serving dynamic web sites or web APIs.
Sadly async is not go-faster-stripes for the Python interpreter.
Under realistic conditions (see below) asynchronous web frameworks are slightly worse throughput (requests/second) and much worse latency variance.
Source: Async Python is not faster, an article by Cal Paterson.