Funnily enough, DC didn't really do a lot with the Pre-Crisis Multiverse concept in terms of giving us different takes on characters or franchises. Earth 2 Superman, Batman etc. were basically a plot device to explain how these heroes were part of both the JLA and JSA, and served as de-facto 'possible future' versions of those characters. But Earth 2 Batman, apart from being older, married to Selina and with a daughter, wasn't that radically different from Earth 1 Batman. We also barely got to see him before he was killed off.

Since we're apparently getting an 'Ultimate DC' in the form of 'Absolute DC' that's where I'll split off one version of the Dark Knight and his world.

Earth 0 - Mainline DCU

-Bruce Wayne is in his mid-to-late 40's. As Batman he is a veteran crime-fighter and globally renowned hero.

-Batman is hailed as the great hero who wiped out organized crime in Gotham and defends it from super-villains, terrorists and other threats. He's a long-standing senior member of the Justice League, one of Superman's best friends and closest allies, and a close friend and ally to the other major Justice League heroes/founders.

-Dick Grayson, in his early 30's, is Nightwing, veteran leader of the Titans.

-Barbara Gordon was Batgirl until she was paralyzed. She's now Oracle. Though spinal implants restored her mobility to a great extent, enabling her to briefly resume the Batgirl mantle, she prefers to stay off the field and serve as a mentor to the new Batgirl Cassandra Cain, as well as leader of the Birds of Prey.

-Tim Drake is a former Robin who has retired from active crime-fighting in the field, but continues to aid the Bat-family and the superhero community as a genius technologist. Occasionally returns to the field as Red Robin.

-Damian Wayne, son of Bruce and Talia, is the current Robin.

-The large extended Bat-family, with a rotating membership, includes - Helena Wayne/Huntress (Bruce and Selina's daughter from an alternate timeline/possible future), Duke Thomas/Signal, Harper Row/Blue Bird, Stephanie Brown/Spoiler, Cassandra Cain/Batgirl, Jason Todd/Red Robin and Kate Kane/Batwoman.

-Commissioner Gordon is in charge of the GCPD, now on the verge of retirement.

-Default Batsuit: 'New Look' blue & grey suit with yellow oval

Absolute DC

-Bruce Wayne is in his early 30's having been active as Batman for the last several years.

-Batman is regarded as an outlaw vigilante by the authorities, though the public and a section of the media are gradually warming upto him. He's dealt a severe blow to organized crime in Gotham, led by figures such as Carmine Falcone and Sal Maroni, but night after night he continues to fight what sometimes appears to be a hopeless battle, even as a new breed of eccentric costumed 'freaks' start to appear. The Justice League doesn't exist yet and Batman, if he has encountered Superman or any other heroes, has an antagonistic relationship with them and views them with suspicion.

-Dick Grayson, in his late teens, has fairly recently become Robin and is about to head to college.

-Barbara Gordon, having just graduated college, is about to begin her career as Batgirl.

-Another notable Gotham vigilante is Helena Bertinelli AKA Huntress who comes onto Batman's radar and falls foul of him.

-Recently promoted Captain Gordon is head of the Major Crimes Unit, and covertly works with Batman.

-Default Batsuit: Year One suit or New 52 armored suit with plain black bat