Just to preface - I have only used Elixir in production and not Erlang.
I would honestly recommend Elixir. This is my opinion and not necessarily the right one for you, but below I will list my reasons why.
- Productivity: I come from a Ruby/Rails background so the Elixir syntax and style is something that was very familiar to me. One of the main factors that helps me determine whether or not to learn a language is how productive I can be in it - mainly why I chose Ruby. Elixir is the same. I can work just as fast in it as I can Ruby with all the added benefits of concurrency and pattern matching.
- Erlang: Since Elixir is built on top of Erlang and compiles down to erlang and the beam vm, you have access to every erlang module and package. So if you are worried about using elixir and missing out on all of the features of Erlang, you shouldn't be. Elixir even has it's own implementations of most of the bigger Erlang/OTP features such as GenServer, GenEvent etc. 
- Community/Resources: The Elixir community is really a great one. The slack channel is really popular and great way to get some answers for beginner questions. There are already some really good books written on the language (Programming Elixir 1.2 - Dave Thomas, Author of the Ruby Pickaxe) also that make getting into the language really easy. 
Really, if you have a mess around with the two you will probably come to the same decision that Elixir is a much nicer language with all the features of Erlang + More. It's on the rise as well, I can't remember the exact numbers but I remember reading something from the Hex website (package manager) about a considerable increase in package downloads.