In Programming Elixir by Dave, he will guide you through all Elixir feature showing you some concepts of functional programming, concurrent programming, and testing. The book is for experienced developers. In Learn Functional Programming with Elixir by Ulisses (what me?), it will guide you only though functional concepts and show you Elixir. The book is for beginners, then a lot of examples will be step by step.
A good example is the "recursive functions" subject. In Programming Elixir you'll have ten pages that describe the recursive function and quickly jump to lists navigation, high order functions, and tail call optimization. In Learn Functional Programming With Elixir, we have entire a chapter with more than 20 pages about recursive functions. You'll see bounded and unbounded recursion, decrease and conquer, divide and conquer, tail call optimization, and anonymous recursive functions. Then, we have another chapter with more than 20 pages to explain high-order functions, giving you several examples from simples lists operations to lazy computation.
I'll hope this explanation help you understand the difference between the two books.