This is gonna rankle folks who like one or the other, but they're basically the same language. When it comes to languages that run on the same VM, Erlang and Elixir are very close together. They aren't nearly as far apart as say, Java and Clojure.

Elixir adds a few things (a lisp-style macro system, protocols, UTF-8 as the default string type, a builtin build tool, streams) but Elixir is not a huge departure from Erlang in the way that Clojure is a huge departure from Java.

By far the biggest things you're going to learn when you learn either one are going to be the BEAM runtime itself and the OTP libraries, which both Elixir and Erlang have in common.