The Amazon Army
If more of the pieces were Amazonian, I'd call this the Amazing Amazons, but hey....In the Amazon Army, the Queen is replaced by an Amazon, a piece that moves like a Q or N (that is, Rook plus Bishop plus Knight), and the Rooks are replaced by R4 -- that is, Rooks that can only move 4 squares.
The Kings, Pawns, Knights, and Bishops are the same as in FIDE chess.
The point of this army is to have a top-heavy material balance. The total strength should be the same as the other armies, but a certain amount of power has been taken away from the Rooks and given to the Queen. Because the material balance is so unusual, I'm listing this under "Chess Variants with Different Armies rather than under "Chess with Different Armies".