From what I've seen... I think if I were writing business applications, I'd reach for Elixir... if I were writing something lower level like communication software, I'd reach for Erlang.

I have written a fair amount of Elixir (and targeting business applications) and I think Elixir's expressiveness lends itself well to making more abstract models of the business processes and data seen in solving business problems. However, writing Elixir I find you end up reading a lot of Erlang and in certain problem spaces I could imagine the appeal over Elixir. I could absolutely see where if I were writing more technically oriented programs.... programs closer to the hardware in some ways or programs designed to communicate with other programs (protocols, etc.) I could see Erlang as being a more clear and direct language in these circumstances.

All of this is very hand-wavy, but it's my impression.