Instead of me listing all the nice things about Elixir which you can read about online, feel free to send me an email with any questions regarding usage in production. I've been using it for some time and I'm very happy with it.
You may want to look at these benchmarks also:
https://github.com/mroth/phoenix-showdown
https://gist.github.com/omnibs/e5e72b31e6bd25caf39a
Here is a post about using 2 million active websockets connections in Phoenix: http://www.phoenixframework.org/blog/the-road-to-2-million-w...
From my experience, Rails and Phoenix speed isn't comparable. Even in development mode (with code-reloading etc) Phoenix is much faster than a production Rails server. I've also replaced three Node.js servers with one Elixir server which did the same work with less memory and CPU usage, but I'm aware that most rewrites have a similar story, so I won't claim that this is enough proof.