I haven't seen the Hal Leonard book. From the description it seems like it must have a relatively short, quick explanation of the system and then gives you charts of 200 songs.

The Chas Williams book has 38 pages explaining the system. So I doubt the Fake book could cover all aspects of the system (though it is not a complicated system). Reading that many charts - the 200 in the Fake book - (if written correctly) could certainly teach you a lot about it.
The remainder of the Chas Williams book (mine has 80 pages total) is handwritten charts from the Nashville elite who were the first to use it extensively...

Pretty much everyone in Nashville learns it from the Chas Williams book. It is the "standard".