What proceeded was a very long, complicated history of the crime families, drama, ups and downs of Gotham City. In many ways, it was very similar to his own Gotham. Some of the players were the same. Falcone could always be counted on. Some were missing entirely like Fish Mooney. Some might be new to him; the Bertinelli Crime family (now mostly deceased) or Roman Sionis (also recently deceased).
There were other players too; she kept mentioning a Mr. J and context suggested that she'd been very close to him, and that Oswald had partnered with him almost as many times as he had betrayed them.
Even some of the names of the cops would be familiar. Commissioner Gordon, Harvey Dent, Harvey Bollock, Renee Montoya. Along with the cops there were the vigilantes, a Batman at the top of the list, Batwoman, Nightwing, Batgirl, about forty different Robins, Red Hood, Huntress. Arkham Asylum mixed heavily into the plot, which at this point had been mostly lost on Harley and was definitely not told in order.
But if Oswald wanted to know about his counterpart, the distilled facts were these—
1. He was much more established in Gotham. Older. Harley didn't know his origin or how he got started. Her Oswald pre-dated her.
2. Unlike a bunch of other crime families and organizations, he had both legitimate and illegitimate business interests and it was often difficult to tell what side he was own beyond his own.
3. Harley seemed friendly towards most people in Gotham. There were a few she didn't like, but those she didn't had a strange tendency to die or disappear from her life.
"—and that's how I convinced you to wear a purple top hat," she finished. There had been no previous mention of said hat, but it made complete sense to her.
Behind them, Bruce continued to chase anyone that ran until Harley let out an ear slicing whistle and it barreled towards them at full speed, all grins. It stopped only at the last second, sitting in front of Harley with a self satisfied laugh. "He's such a good boy," Harley said to Oswald. Bruce certainly seemed to agree.