The Baseball Prospectus is an excellent resource, and a fun browser for baseball fans. The Pecota projections give a sense of how the player might perform THIS year, and whether he's more likely to improve or decline from last year. The little analytical paragraph on each player is priceless, and often very funny.
On the other hand, there are a couple of problems...
The first is the authors' theological insistence on not allowing the stats for Runs Scored, RBIs, Wins-Losses, or Saves to show up anywhere. We all get it, these stats are problematic and subjective and don't always reveal the true contribution of a player to his team. But hey, those are all stats that every single fantasy league in the country counts. So the tens of thousands of guys with fantasy teams who are looking for some insights into some of the key statistical categories will be disappointed. This book, open alongside of the Bill James Handbook, should give you all the data you need.
The second problem is really about the format. The Bill James Handbook lists all the players alphabetically, and that makes sense for fantasy coaches. The Baseball Prospectus, however, lists the players by team. But even where a player has changed teams and the authors note that fact, the Prospectus insists on listing him with his old team.
I think the Bill James Handbook --because it uses the stats and format most convenient to fantasy owners-- will be a better buy if you're only getting one book. Fantasy owners are less interested in the collection of talent on any particular real-life team than in being able to assess the whole universe of players. So the Bill James book is better-suited to fantasy owners.
On the other hand, the Prospectus --because it groups players by team and doesn't bother with some of the key fantasy stats-- is probably more suited to the guy watching a game on TV who wants to read about the specific players on one team. The Prospectus's statistical analysis showing the value of a particular player to the team and park he plays for, and vice versa, also support the notion that this book is better-suited to someone focused on one team or game.
In short, both books have strengths and weakneeses. I bought them both and enjoy them side-by-side. But it depends on what is your primary interest.