I decided on a sports metaphor for naming this army, and so we have
The Colorbound Clobberers
as the name of the new team, and
The Fabulous FIDEs
as the name of their opponents in this game.
This piece is usually a little bit stronger than a FIDE Rook, for most of the game, in most positions; and potentially noticeably weaker than the FIDE Rook in some late endgames.
This piece is usually slightly weaker than the FIDE Knight; it moves in a clumsy manner, but is extremely strong when it can get to a good position.
This piece is stronger than the FIDE Bishop, by a fair amount.
Of course this piece is weaker than the FIDE Queen, but it is stronger than you might think.
The BD is obviously stronger than the FAD, but not by much. In practice, you can treat these two pieces as being of equal value. The BD is obviously stronger than the N, and the FAD is also stronger than the N. How much stronger? Who can say...
The BD should be thought of as equal in value to the Rook. The FAD is presumed to be weaker than the Rook. How much weaker? Who can say...
The Clobberers are a team with a weak "Queen" but an overstrength "Bishop". The weakness of one makes up for the strength of the other. There are disadvantages to having so few weak pieces, of course, and advantages to having a weak "Queen" (for an example of this, look at move 19 of FIDE-CC-02.html where White chose not to trade Q for NB, and thereby lost his King).
If you just look at the values of the individual pieces, the Clobberers seem to have the advantage. Add to this the fact that the Clobberers can develop quickly, without moving too many Pawns, and things begin to look sticky for the FIDEs.
On the other hand, the Clobberers are awfully colorbound. They can easily get into situations where all their strength is concentrated on squares of a single color, leaving them either unable to exploit an advantage or vulnerable to attack on the other color.
The real equalizer is the hard-working, straightforward, and steadfast FIDE Rook. This piece has great endurance, and actually gains strength as the game goes along. I have seen games where things looked bad for the FIDEs from the opening kickoff, and seemed to be getting worse and worse, until suddenly there were just a few chessmen left standing on the field and the Rooks began scoring goal after goal.