I think both of these books cover the same stuff. Better buy one of the two and the Phoenix book.
What I did is after reading Programming Elixir, I went through the guides on http://elixir-lang.org/ to refresh what I learned, and it turned out perfectly!!
If you want to buy 2 books for Elixir I would recommend one of the introductory and then Elixir in Action.
Although many people have already answered in this topic, I want to offer my two cents, as I am of the opinion that JavaScript is a really bad language to start out with.
I think Elixir is a really wonderful language to start out in, because when you start out, you don’t have any patterns that you need to unlearn. Many people that come from other contexts (especially non-functional ones), face this when starting with Elixir. (Although it is a lot easier to migrate to Elixir than, say, Haskell).
The main argument in favou of JavaScript I’ve heard so far is based on bandwagoning (i.e. ‘learn it because everyone uses it’), which is an argument that hampers innovation. Javascript itself is (arguably) a terrible language (to start out in), because it has many peculiarities that only exist for historical reasons; It is very easy to write incomprehensible, unmaintainable and/or unsafe code in JS.
I think it is better to learn programming in an environment that actively points you to a way of writing understandable and maintainable code, because once you’re used to doing this, you will carry that over to other languages, including the ones that might otherwise seduce you to write in an unmaintainable way.
Agree with everything you said except for recommending Programming Elixir. Programming Elixir is not beginner friendly. Introducing Elixir may be a good starting point before jumping into Programming Elixir.
yep )
i’d agree with this
i’m a newbie for myself (half a year online courses and half a year working as RoR junior developer)
and i agree completely that Programming Elixir is not the book for a beginner… i started with it, but after about 30% of the book i just can’t move forward and switched to Introducing Elixir, which is much easier…
now i’m back to Programming Elixir
in my opinion this book is for experienced programmer learning new language, not for a student learning programming from zero (even not for learning with some small experience in programming)
I can definitely see your and @max-underthesun point. I have not read Introducing Elixir and though it would be about the same. Thanks for pointing it out.
You mentioned that you are an ROR programmer. Does knowing Ruby and ROR first help you learn Elixir?
Any way, thanks for the suggestion, I will read Introducing Elixir first.
i’d say it helps and it making it more difficult simultaneously ))
it helps because a lot of things about programming you already understand and not just understand like theory, but you know exactly why you may need this function or this “way of doing” (pattern) in development…
and on the other hand, like people already pointed here “your first language has an incredible impact on how you think about programming”… and it can be a real pain sometimes to understand concepts of a new language, especially if your first is from another programming paradigm
in my case Ruby is a kind of language you can start programming without any knowledge of “any real programming stuff” 
… all you have to do is to learn some syntax and use some common logic…
Elixir seems to me more “mathematical” and more “programmatical”… especially if you are starting from Programming Elixir, not from Introducing Elixir 
(and this is exactly what i was looking for)
The 2nd edition is available as an Early Release right now: Introducing Elixir 2e - O’Reilly Media
Do you know if they do free upgrades like Pragprog? I have the first edition but still haven’t got around to reading it 
I’m in the same boat. There used to be an option on your account to upgrade to the newest edition @ 50% discount but I haven’t seen that for some time. I’ll probably monitor and post if it becomes a “deal of the day” or another relevant 50% sale comes along.
That being said as “member” (i.e. account holder) there is the buy 1 ebook, get 1 free; buy 2 ebooks, get 2 free; buy 3 ebooks, get 3 free; and so on… code - in case you are buying anything else.