asyncio is more modern, more stylish, and more concrete.
Twisted is more timeless, more patterned, and more self-aware.
I can imagine Twisted's asyncio reactor becoming its default (and the Twisted flow control slowly declining in importance), but Twisted's protocols, control structures, and execution models becoming more popular.
Twisted has undergone a great resurgence in quality engineering since asyncio became more viable - this was surprising to me, but is actually probably reasonably consistent with the way the historical influence of the standard library.
Overall, I think that Twisted is a great project; I almost always reach for it when my python codebase becomes mature enough to need more thoughtful abstractions around network I/O.