In the same vein of the Gotham City 2100 story I still may or may not write is this. In this slightly different continuity, Super-Girl is a young adult just starting out and Bat-Girl (Angelica) has been at it for a few years. Super-Girl is still the daughter of the current Superman, just a couple of years older. Anyway, without further ado...
What is the Difference?
Gotham. A crime infested cesspool of corruption and hopelessness. For a time there was someone to watch over it. Protect it from those who sought to bring it harm. The Dark Knight Detective. The Infamous Batman. But he is gone now. Thought of as nothing more than a bedtime story, used to frighten children into keeping in line.
Between a Vigilante and a Hero...
Metropolis. The gleaming city of tomorrow. The pinnacle of human advancement and a shining example of what can be accomplished through the power of the human mind. Represented by the Man of Steel for a time, the savior of this city has now disappeared. Superman, the Man of Tomorrow, has vanished without a trace.
Between a Villain and a Criminal...
But these cities are not without their champions. Atop one of Gotham's tallest of buildings stands a brooding figure of a bat, watching over Gotham from a gargoyle, a tattered cloak flowing in the wind of that rainy night. And in Metropolis, a familiar gold insignia pressed against the back of a crimson cape shines bright over those who would pray for protection. Even the City of Tomorrow is not without its tyrants and there is still someone remaining to protect it.
This female paragon of morale adjusts her head to hearing a cry for help then flies off in a hurry to meet whatever dangers she may face.
The woman dressed as a bat sees the emblem projected against the clouds and narrows her eyes, expanding her cloak and gliding off into the city.
The World's Finest Heroines
Several crooks march through what seems to be an abandoned museum at night, armed to the teeth in advanced weaponry. One of them stops in his tracks and looks over his shoulder at the skylight overhead, almost sure he'd seen a shadow pass by overhead.
The crooks manage to arrive in the central room where they eventually find what they are looking for. A green, crystal ring. It then becomes fully apparent where they are. All around them is equipment lining the walls and in the display cases. A cowl, a vehicle, a golden belt. All of it sported a very distinct emblem.
One of these thugs reaches in a picks up the ring before it is suddenly stricken from his hand by a mysterious projectile that lands at his feet. He then turns and looks up to find a black booted heel suddenly meeting his face and the next is soon blinded by a shadowy black cloak.
The bat stands over her quarry and notes that one of the thugs had disappeared. The ring had been taken. After looking over every other thug, she finds a picture on one of them. A picture of the Girl of Steel. With that in mind she throws the picture over her shoulder and departs. Someone was after the last Kryptonian and Gotham was stuck in the middle. She didn't enjoy that.