Regarding the Queen + Knight piece (amazon):
Sometimes having too much power is not a good thing. I experimented with an Amazon piece in the earlier days, i.e. before the year 2000. In my experience, it "attracted too much attention."
1. Because it was so strong, literally every piece on the board could attack it, and every piece would want to attack it, because winning it was tantamount to securing a large advantage.
2. Deploying the Amazon too early would therefore lead to collosal loss of tempi, almost always fatal even in the Amazon was not exchanged for inadequate material.
3. Deploying the Amazon too late would mean the other side's Amazon was "running rampant", scooping up material (usually many pawns.)
4. When deploying the Amazon "correctly", it would most often just end up trading itself for the opposing amazon!
So, after all of this experience, I found that games with Amazons were very "Amazon-centric." By that I mean they were the focus off most of the strategy and tactics of EVERY game. Either you tried to run down an Amazon developed prematurely, or you tried to time the development of your own Amazon so that it could win all kinds of material while your opponents' was misplaced/undeveloped, or you simply aimed to trade them off the board.
Then, once Amazons were off the board, there was this "empty" sensation. It is like going from racing on the Autobahn with a high performance sports car, to walking knee-deep in the ocean! A very abrupt change of pace!
In the end, we decided too much power was not a good thing.
The Archbishop and Chancellor pieces don't suffer from this distraction. Their own characteristics allow you to create long range strategy. Because of its solo-checkmating possibilities, the Archbishop is the deadliest piece in the opening. Just look how the Archbishop threats dismantled ChessV in only 27 moves in this game:
http://www.gothicchess.com/javagames/db ... 7/game.htm
Look particularly at 19. Qxh5!! were black can't even take the Queen with a Pawn since the threat is Ah6#!!
The Chancellor tends to be the dominant piece in the middlegame, althought it too can be used to accelerate the endgame. Here is how Vortex mated SMIRF in 28 moves by sacrifcing material and using the Chancellor:
http://www.gothicchess.com/javagames/db ... 1/game.htm
Note that a Chancellor and Bishop used in conjunction are a deadly combination, as the complete what is "missing" from each other. The Chancellor + Bishop is essentially the "Amazon" piece you spoke of earlier.
The Queen is the strongest of the 3 pieces in the endgame. While an Archbishop can be used somewhat early, the Chancellor and Queen are used like they are in chess. Put in play too early, and they can be attacked without mercy.