When a friend saw me carrying this book, he asked me, "So, what is the verdict?" Maybe I hold back my one-cent until the end. For now, let's review the book first. It has 17 chapters, detailing various aspects of the battle between bishop(s) and knight(s).
Chapters 2-4 show the traditional techniques to handle the bishop-pair and knight-pair. Chapters 5-8 clarify the problem and over-rating of minor pieces.
Chapter 9, 10, 12, and 13 provide us some tactics and strategies to change the position dynamics, and some sacrifice to gain some critical tempi.
Now, from personal experience. When I was a weak beginner, I often lost too early in the opening before the bishops could be fully utilized. Together with bishop's single color control, I felt the knights were stronger. Then from the teaching of Chernev's, I learned the strength of bishop-pair; and later learned two main themes. The first one is: in middle-game with packed center, the knights are stronger; with loose center, the bishops dominate. The other, generally in endgame: with pawns on both sides, the bishop is preferable; pawns on one side, bishop can at least hold a draw.
Most GM like Botvinnik, Smyslov, and more prefer bishop-pair; while Chigorin, Reshevsky prefer knight-pair. However, they all can handle any combination of minor pieces skillfully.
So, what is the verdict? The answer is their "relative space control with respect to other pieces" on the board. For example: without the queens, the long diagonal control of bishop(s) plus the rank and file control by the rook(s) (especially aiming at the enemy king) the bishop is stronger. Mayer mentioned this in chapter 16, the Grindable Ending. While in a crowded position (especially with many pawns) the knight is preferable. If somehow, the knight can established a strong outpost for a king-attack, with the penetration of the queen, the power of the knight can be decisive (Mayer: chapter 17, Capablanca's Theorem). Likewise, the position of the pawns (friends or foes) could magnify and/or neutralize the bishop's strength; and the pawns can dislodge the unprotected, far advance knights.
Therefore, my one-cent summary is:
a) Relative board control of the bishop and/or knight with respect to other pieces and pawns.
b) Knowledge/experience of different types of these positions.
c) Player's comfort and confidence in handling these minor pieces.
And this personal opinion is not totally conclusive either.
This is one of the first few books dealing solely with this difficult topic. I recall Pachman's Complete Chess Strategies having some sections dealing with this topic too. Both Mayer's and Pachman's books are for very strong (and master) players. Silman's Amateur's Mind gives lighter version and for single minor piece combat.
This is a five-star book.