I actually didn't see the Joker in this universe as a dark mirror to Batman. Joker gave me the impression that he was simply sick of Gotham pretending to be something that it wasn't. Additionally, I took it he had a beef with the mob. His backstories all had SOME element of truth I believe. Given that he robbed a mob bank, I feel they had a hand in his creation. Therefore his use of the mob to bring down Gotham's White Knight in Harvey Dent and cause its citizens to slaughter each other.
Bane would work as a dark mirror to an extent. Bane is said to be a brutal and intelligent character (Gill's words). Perhaps at the beginning of this movie when Batman is dealing with the mob, his methods have become a bit more violent due to the stress of the GPD pursuing him even as the mob continues its shenanigans.
Cue Bane's appearance in Gotham and the maelstrom of rage he'll unleash. Maybe his methods to catch Batman--or achieve his goal--are indescriminate in taking out city property, civilians, or anyone who's in the way. And unlike the Joker, Bane wouldn't announce his plans. He would let them speak for themselves.