Buchwald and Josefowicz specialize in the history of ideas, as shown by their previous book
The Zodiac of Paris, about how artifacts from ancient Egypt became focal points of the ideological struggles in post-revolutionary France. Unlike that story, the story of the decipherment of hieroglyphs has been told many times by other authors. This book benefits from Buchwald and Josefowicz's talent for scouring 19th-century primary sources. But their focus on the beliefs and intellectual backgrounds of the two protagonists, Young and Champollion, means the story gets bogged down in details and digressions, like Young's early studies of vision or Champollion's search for the Roman town of Uxellodunum. While it succeeds as an illustration of intellectual life in Europe during the Age of Revolution, it succeeds less well as a story.
However, that primary-source research cannot be discounted. The story of Champollion's work has long suffered from uncertainties about the timing of his insights that seem to date back to Hermine Hartleben's 1906 biography, or to the Champollion family lore on which she drew. Buchwald and Josefowicz delved into the scholars' unpublished notes and drafts, and are thus more clearly able to follow the timeline of their thought processes. I am personally indebted to their efforts; I'm the Wikipedia editor who researched and rewrote the article about the decipherment of ancient Egyptian scripts, shortly before this book was published. After I got this book, I was able to correct and clarify some small points in the article, and sound a more cautious note about the most dramatic episode in the story.
With their thorough research, Buchwald and Josefowicz may have the last word on Young and Champollion for a good long while.
Jason Thompson's history of Egyptology notes that Champollion is over-covered compared with other Egyptologists, and I hope now that historians will turn their efforts to those lesser-known characters. (The most obvious one after Champollion's death is Karl Richard Lepsius, a titanic figure who still has no English-language biography.)
If you're looking for a description of the decipherment that makes for a better story, I recommend John Ray's
The Rosetta Stone and the Rebirth of Ancient Egypt, which is eccentric but extensive, and Andrew Robinson's biography of Champollion,
Cracking the Egyptian Code, which doesn't use all the sources Buchwald and Josefowicz had access to, but still treats the points of uncertainty with reasonable caution.