It depends on if you're CPU bound or IO bound. If you're CPU bound - switching to an async based web framework may not help that much. If you're IO bound, and you're using synchronous web workers that are sitting idle waiting from responses from databases, etc... an async approach might work better. I don't necessarily think asyncio is the answer though, when you can just (for the most part) drop in gevent or eventlet which provides coroutines that you can use as light-weight threads that can perform IO bound work concurrently with out much change to your codebase.
At work, we use Flask+Gevent for our HTTP API. It's worked pretty well so far!
At work, we use Flask+Gevent for our HTTP API. It's worked pretty well so far!