Pair this book with Nathaniel Popper's "Digital Gold" and it will give you solid background knowledge of Bitcoin's history, the players involved, and the various dramas that happened along the way (Silk Road, Mt. Gox, BitInstant, etc.).
"Bitcoin Billionaires" is a faster read, better paced and written like a novel, and it tells the narrative largely from the standpoint of the Winklevoss twins and Charlie Shrem. If you've read Mezrich's "Bringing Down the House" you know he's a good writer with a good sense of how to pace and arrange a story.
"Digital Gold" is more like the type of history a journalist would write, which is exactly what it is: Popper covered Bitcoin and many of these events for the NY Times. Both good reads, both well-written.
PS: One final, unrelated thought: You'll come away from this book with a good understanding of Mark Zuckerberg's ethical compass (actually, his lack thereof). It makes it extremely difficult to justify actively using Facebook.