If money or portability are your primary considerations, then get a used copy of the first edition, as it communicates the central ideas in an almost identical fashion and is easier to carry around. However, if a few more dollars and a slightly-bigger book don't bother you, consider buying this new edition, as it's subtly-revised diagrams and improved explanation of key brain science concepts make it easier to understand on the first read. For more detail on the differences between this and the previous edition, read on...
Both books are hardcovers and much of the content (including, sadly, the Resources listed in the Appendix) is the same. However, there are a number of important differences between these editions:
At 8.2 x 8 x 1.3 inches, it is bigger than the first edition, which clocked in at 7.1 x 7.1 x 1 inches. While this does allow for the pictures to be bigger and slightly easier to see, it also means a larger, oddly-shaped book to carry around. This only matters if, like me, you like to schlepp your favorite books around and carry them on the bus.
PAGES & TEXT
Includes more pages at 304 pages, rather than the previous edition's 278, making it a mere 0.2 pounds heavier. 10 of those additional 26 pages are the new "Appendix A: The Ten (and a Half) Commandments of Visual Thinking." This is a very useful set of 11 rules of thumb to keep in mind when applying Roam's visual thinking technique. Most, if not all, of these rules are mentioned elsewhere in the book, so don't let this appendix be your only reason for purchasing the newest edition. In addition, these 11 rules are summarized nicely in a slideshow elsewhere on the internet ([...]/visual_think_map/the-10-12-commandments-of-visual-thinking-the-lost-chapter-from-the-back-of-the-napkin). Nonetheless, it is helpful to have them laid out, visually, in one place. Another 8 pages are the new Foreword, which explains Roam's experience of visually attempting to sell the idea for this book to the publishers at Penguin. While interesting and a good example, it is also not a reason to buy this edition.
COLOR & PICTURES
Instead of just black text/pictures, red is now used to highlight chapter headings and subheadings, as well as help readers distinguish between parts of Roam's originally-all-black illustrations and diagrams. This is astonishingly helpful - as it is much easier to understand his diagrams at first glance. Given the table on page 66 (identical to that on page 72 in the first edition), it is no surprise that a small change in color makes it easier for our eyes to distinguish among the parts of his diagrams. In addition, he has added some additional sketches in the book to better visually explain some of his concepts. I was particularly impressed by his improvements to chapters 4 and 5 on how to look better and see sharper. Both his pictures and his text in this section have been revised to provide more clarity for potentially-confusing sections that are partially dependent on communicating a few key brain science concepts. His diagrams illustrating the 6 ways of seeing/showing are also a bit clearer than in the first edition.
OUTLINE OF BOOK CONCEPTS
For an outline of the major concepts in the book, see my blog post ([...]/blog/review-back-of-the-napkin-solving-problems-and-selling-ideas-with-pictures-expanded-edition-2009) for more details.