When we released the 3rd edition, I wrote up a blog post about what changed: https://www.bignerdranch.com/blog/whats-new-in-android-programming-the-big-nerd-ranch-guide/
For some people, the 2nd edition will work well. Others may want some of the recent changes. There are two groups of people who I would recommend upgrading from the 2nd to 3rd edition:
A) Beginners who are cautious about learning a new platform and want the experience to be as smooth as possible. Many of the changes in the 3rd edition make the book easier to work through. We teach our Android Bootcamp class based off of the book so we've seen many, many people work through the chapters. We see where people get stuck. What things come naturally and what things do not. The 3rd edition adds a lot of polish to these kinds of areas of the book.
B) More advanced developers. We've added some new patterns
in Android development to the 3rd edition. For example, we talk about the MVVM architectural pattern and data binding (along with unit
testing). We also talk about ConstraintLayout.
I think the 2nd edition is a great starting point and will get you up to speed with Android. If you fall into one of the two buckets above, I would recommend the 3rd edition. I hope that helps!