There may be two pieces such that they are of equal value, but one always beats the other. Rock breaks scissors, scissors cut paper, paper covers rock....
In the game pitting Bishops versus FADs, you might notice that the Bishops, despite being weaker than the FADs, were able to do quite well for a long time by taking advantage of their long-distance powers.
Conversely, with a Pawn blocking c4 a Knight on f4 dominates a Bishop on f1; Bishops and Knights can dominate each other.
A Rook can dominate a Knight, but cannot dominate a Bishop; because of this, the Pawnless endgame of Rook-versus-Knight is much easier to win than Rook-versus-Bishop.
The WD is about as strong as the Knight, but the Pawnless endgame of K+WD versus K is a win. Therefore, the endgame K+WD+P versus K+N is almost always a win.
This gives the WD a certain advantage in the endgame, which helps make up for its other weaknesses.
However, there are many ways to relate to Pawns.
Bishops and Pawns defend each other nicely, but then have trouble advancing; a Knight can defend a Pawn, or help its advance, but not both at once (and yet Knights and Pawns do work well together in general); Rooks can get behind and push, but then cannot attack the advance-square, or they can get in front and pull, but then they get in the way at the end. The clumsy WD can run a Pawn down to the goal line, but is a bit slow; the WA is not a good shepherd.
In FIDE-chess, Knights are mutually stealthy with everything else.
I have found stealth to be less important than I had expected.
I wonder if you could design two armies such that one would be noticeably stronger than FIDE-chess, the other weaker, but when they fought each other the weaker would have an advantage...