I have no experience with either (though I have perused some Elixir docs a while ago). I'd much rather jump into a Phoenix/Elixir project though, just based on what I've heard and know about it.

I wouldn't apply to a C# job, I have no interest in it.

I think the only disadvantage is really that Elixir devs would be newer to Elixir. But I think the applicant pool would skew towards having broader experience.