I would choose based on several criteria:
[experience]
If you are not familiar with asyncio, tornado or Twisted, and you're supposed to build a production-ready system that should have been ready yesterday, then don't do it async. Also, if the async paradigm itself is new to you (not necessarily in Python, but with other languages too), then I wouldn't use async either.
[ecosystem]
If what you're creating will be used as a library and incorporated in other code - then do it in a way that makes it easier for that other code to leverage your new logic. For example, if this is supposed to "click into" a thing that uses one thread per connection, then follow the same ideology.
[performance]
Async servers will probably deal better with N clients, but this might only become relevant when N is a very large number. Think about your performance expectations.
Alex