The thing about the Bird of Prey is that it is so small. When you take the weapons and shields of a big ship and put them on a flying, cloakable power core, you get a ship that, pound for pound, outstrips nearly every other ship out there. The Defiant is the only exception I can think of that might be superior. The Jem'hadar ships were equal or inferior. I bet 3 B'rels (inStar Trek) can take out just about any one ship out there, and be built for 1/5 the price of that ship.
The Dominion, clearly a capable military force that conquered their entire quadrant, also realize that little flying weapons platforms make excellent mainstays of a battle fleet.
W.