Elixir, being a BEAM language, is designed for highly reliable and low-latency concurrent network services. There is a tradeoff between concurrency and within-task performance, in which Elixir favors concurrency and Julia doesn’t.
Clojure is a lisp on the JVM. It doesn’t have the same numerical focus that Julia does, but it has a nice design and the huge JVM ecosystem behind it. There’s a lot Julia could learn from Clojure, like its Spec system. Transducers.jl is inspired by the same feature in Clojure.
Both languages are functional, which I hope Julia will do more of.