The history is muddy, honestly, but I can't find any source that doesn't list Ameraucanas as rare.
Thanks for that last line though, I learned something from it. Apparently both Araucanas and Ameraucanas were derived from "Easter Egger" chickens (though at the time all were just called Araucanas). I did not know that. However, I think it's a bit of a stretch to say that either breed was developed from the current strains of Easter Egger, since they both come from the 1920s-30s and more recent Easter Eggers are often hybrids or have been crossed back to the standardized Araucanas or Ameraucanas (hence why I say muddy).