The performance question is a good one. Erlang has never been a performance wonder, so I'd be surprised to hear that Elixir is noticeably faster than Ruby.
In that case, the multithreaded nature of Elixir and the VM there's no comparison.
I tried searching for raw ruby+erlang benchmarks but couldnt find much in the short time I looked.
If we're talking about pure ruby and elixir, things become complicated, you can do some stuff a bit faster in ruby sometimes (where ruby is using native optimized C code)
DHH even acknowledges this: "But sure, I'd like free CPU cycles too. I just happen to care much more about free developer cycles and am willing to trade the former for the latter."