After reading both of them, I slightly prefer ‘Elixir in Action’ over 'Programming Elixir`. I think EiA does a better job explaining some of the core concepts, and goes into more detail than PE. PE, however, might be a more gentle introduction to the language.
These books are both excellent, and either should give you a good understanding of Elixir.

The same question was recently asked on Devtalk - here’s a copy of my reply from there:

You can’t go wrong with either, so if you can only get one, go by whoever’s writing style you prefer

(Btw if you’re interested, Dave Thomas is thinking about running a book club on Devtalk for his book - if that interests you let me know!)

Thanks for answering! And, I don’t know if I will be able to join a book group. You know, I don’t really have a lot of free time