John Trewin's
House of Special Purpose* isn't bad -- it includes photos and information that haven't been printed elsewhere -- but it does contain some myths about the Ekaterinburg period that have been disproven by more current research. Generally, though, you can trust Gibbes' memories of Tobolsk.
Last Days is definitely a more reliable account of the Romanovs' captivity in Ekaterinburg. It's also more scholarly in tone, more critical of the Romanovs themselves, and pays more attention to the political climate outside the Ipatiev House than most other books.
It depends on which period of captivity you're more interested in -- Tobolsk or Ekaterinburg -- and what style of narrative you prefer. Trewin's tends to be personal and anecdotal, and his book is more richly illustrated. Rappaport is more objective and analytical. They both have value.
(*I believe there's also a novel called "House of Special Purpose" but I don't recall the author's name. That may be the book that the other forum members didn't care for.)
