This was the most extravagant of my many book purchases in London last week, at £16.50, and to be honest I would have preferred to wait for the paperback. These are good stories, though, with interesting parallels between them: Turtledove and Gentle pick the Mediterranean for their setting, Stirling and Williams choose the nineteenth-century American West; more to the point, both Turtledove and Williams tell the story of their point of departure by injecting a real philosopher into a contemporary conflict at which they were not present in our time-line (Turtledove sends Socrates to Syracuse with Alcibiades, and Athens becomes a dictatorship and major military power; Williams rather more daringly puts Nietzsche at the OK Corral, though the historical consequences seem likely to be less serious) while Stirling and Gentle tell side stories from their own well-established Alternate Histories (respectively a glance at Texas in the world of the Peshawar Lancers, which I have not otherwise read, and the origin of the title character in Ash: A Secret History, which is superb).
In fact a characteristic more firmly shared by these stories than their Alternate History pretensions is that all four are very firmly in the tradition of military fantasy stories. Stirling and Williams basically tell of different militias slugging it out on the Texas/Arizona frontier. Turtledove tells of the siege of Syracuse and then has Alcibiades attacking other cities. And Gentle's piece, the best of the four (and showing despite my earlier worries that Ash was not a one-off) is a meditation on women as warriors and the difference between historical and contemporary perceptions of them.
Turtledove's story is competent; not as good as my favourite piece of his, "Down in the Bottomlands", but well ahead of his execrable WorldWar. Williams' tale is amusing but doesn't really shed any extra light on history except to make the point that given all the other strange people around in Tombstone that day, Nietzche would have fitted in fine. Stirling's piece is far too rushed and ends too quickly.
Summary recommendation: look out for Gentle's story in a different paperback anthology.