Greatest Chess Enigmas: Knight vs. Bishop
This is one of the greatest mysteries of chess, and had, up until fairly recently, baffled chess greats as well as amateurs. Chess theorists have discovered that we were asking the wrong question. The question is not "which is better". The question should be "when is it better". You see, it all depends on the situation.
In an opening, a knight is better when:
-it is the first move, since the bishops can't move
-when the pieces are still developing (knights before bishops!)
-if the knight is centralized, on its "happy square", or really on any square that has multiple targets in the center
-don't forget - a knight on the rim is dim!
In an opening, the bishop is better when:
-it has multiple attacking squares
-a nice diagonal
-a bishop pair is always beneficial
-the bishop is aimed at the center
-if your pawns compliment the color of the bishop(s)
-don't let your bishop get trapped!
In the middlegame, not much needs to be said, since the benefits are almost the same. A closed position favors the knights, while an open position favors the bishops.
In the endgame, the bishop usually dominates the knight, since the knight is slow. However, if the opponents pawns are on the opposite color of your bishop (and vice versa), then you are in serious trouble, since the bishop cannot change colors, but the knight can.