I've just passed my exam on Theory of Computation, and I've used both editions of this text. Frankly speaking, I couldn't choose one of the two should I keep only one of them.
Whereas the first was full of strict formalism, the second has traded this for a more discursive approach. Whereas the first reported theorems name (of their authors), the second has traded this for a richer bibliography at the end of the chapters. And more objectively, the first edition covered more "classical" topics with shorter treatments than the second, but this last treats survived topics with richer details (starting from the first chapter on mathematical basis for the course) and with updated examples of applications (XML and Markup Languages, e-commerce for DFA, etc).
This said, you know why I can't decide. A discursive approach is of course always desiderable, especially if you're completely new to a subject, but a strong notation is helpful in my mind because it improves communication and removes ambiguities. Hence, the best approach would probably have been a mix of the two, or halfway the two.
As a second matter, having a rich bibliography is surely helpful both for further studies and as a reference, but it's quite tedious to look at the index and be unable to find something like "Kleene theorem": you've to dive into bibligraphy to discover that "L is an L(DFA) if and only if it also is L(REG)" is something that has been studied by Kleene.
Finally, I surely can't question the reduction of the complexity theory part since it is in the right of the authors to remove "optional topics" (if you use the book for a course on Theory of Computation only) and give a more focused target to the book, but removing stuff like the Myhill-Nerode theorem make things annoying since virtually every course on Automata theory and Computation includes it (like my one did, as well as the course on Languages and Compilers), so you have to look for it elsewhere if your only one book is this second edition.
I would give four stars, should I keep in heavy account the radical changes they made over the first edition and that includes the removal of some stuff, important on my opinion. But ... as this is just my opinion, and since it is a very well written and informative book (rich of many details that other texts lack of) and surely one of the bests in the area (I've had 4-5 books in my hands for this course), that's why I gave it 5 stars.
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Introduction to Automata Theory, Languages, and Computation: United States Edition
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