The paradigm of Erlang is message passing. The primary idiom is logic programming (like Prolog). Functional programming is related to logic programming. Between message passing, logic programming, and simple primitives for concurrency; Erlang programs tend to look a little strange. But it all hangs together in a way that has been field tested for thirty years. Erlang is a language that was engineered for use by engineers for solving engineering problems.

Elixr is mostly a way of avoiding learning Erlang and making the Beam VM popular. It is a procedural programming abstraction layer. For me, Elixr's abstractions generate an impedance mismatch and Erlang's syntax better expresses the engineering mechanisms of concurrent systems and logic programming. YMMV.