According to some benchmarks, an ASGI framework will generally perform better than a WSGI framework [1].
Currently, the ASGI ecosystem isn't nearly as mature as the WSGI ecosystem, and for a production system, I would still prefer WSGI for now. Django just got ASGI support in 3.0, but it still has a long way to go to become fully asynchronous [2]. I think Starlette [3] will become a popular ASGI framework, but it's still early in it's development.