- The Syntax and Learning Curve
In Go you can start after studying about 1 day since the syntax really similar to C (most universities taught C-family language), you can feel productive right away.
In Elixir you'll need more than just 1 day (and obviously exponentially more to get the feel in Erlang unless you've learned about Prolog and LISP before), the syntax is somehow similar to Ruby, but you also required to learn about FP concepts (just like another functional language: Haskell, LISP, Clojure, F#) that could make you a better programmer. - Concurrency and Deployment
In Go you can achieve faster concurrency for single machine, but at cost of memory usage for the same amount of unprocessed light-thread (about 2-2.6x, see the edit history of previous link). If you need to need more than one machine, you must do it manually (but it's easy since Go statically linked: just a simple scp and executing service script would do).
In Elixir you can have distributed concurrency, as described by many Erlang expert, BEAM is a 30 years old battle-tested virtual machine, that has these built-in advantages: - Lightweight user-space threads (Goroutines requires more memory)
- Built-in distribution and failure detection (not sure what's the comparable library in Go)
- Reliability-oriented standard library (in Go you must check every error)
- Hot code swapping (use endless in Go to achieve zero downtime)
- Raw Performance
In Go you got raw-performance, similar to Java, but more memory efficient, for any CPU-bound tasks, you should prefer Go instead of anything that currently has slower implementation (Javascript, PHP, Python, Perl, Ruby, Erlang/Elixir), see the 16k concurrent user column.
In Elixir or any other BEAM language, since the light-thread have smaller memory usage, you can handle more process at the same time. - Hiring
Since Go are relatively more popular (because it's easier to learn) in terms of number of job postings I've encountered, TIOBE index (Jan 2017: Go #13, Erlang #44, Elixir #66), GitHub popularity go vs elixir, or Spectrum (Go #10. Erlang #35); than other BEAM-based language (especially Erlang), if you are PM/VPE with tight deadline, I believe Go is the better choice at this moment
So what you should use for your next project? It's always depends on what's the use case (right tool/person for the right job) and the deadline, there are no silver bullet. And no I don't intent to start a flame war.