Having worked extensively with both Erlang and Elixir in the last 7 years, the main advantage for me has always been the smaller code base that those projects tend to produce when compared to other languages. Especially for projects that have some long-running components to them the Erlang built-in features allow writing really short yet fault resistant systems.

The Supervisor system, the per process garbage collection (no stop the world), 'start_link', "Let it crash", and pattern matching are for me the superpowers of beam. Elixir is contributing a great package ecosystem, 'mix format', and better features for the new live web of websockets