Here's my two cents.
I'm a big supporter of the idea that Talia and Bane are equals and co-Big Bads of TDKR, and I believe the idea is strongly supported in the film. Some audience members discard all of Bane's previous monologues after the reveal, believeing that he was going out of his way to decieve Bruce and the audience about himself. I think that's wrong. All of Bane's speeches to Dagget and Bruce hint at a fanatical devotion to Ra's Al Ghul as his savior, role model, and ultimately some very twisted self perceptions.
Bane's whole demeanor and personality are pretty clearly cut from the same cloth as Ra's, but cut up crudely with broken scissors. Both men have a measured, verbose method of speaking, both have a veneer of gentlemanly manners around a ruthlessly cold interior, and both are highly charasmatic leaders of the League. But whereas all these traits are genuine in Ra's, Bane's are an imitation that's just kind of naturally more barbaric than his master. Bane's favorite posture-holding the lapels of his jacket or straps-is first shown in Batman Begins by Ra's doing the same thing. In the same way that Bruce's graying hair and beard draw a visual parallel with the "Ducard" persona of Ra's, Bane's personality parallels their mutual mentor's true self and ninja master manner.
Bane quite clearly holds to the League's goal of killing Gotham, which as other's have noted, is meant to be more of a strike against the world, to begin "the next era of western civilization." Bane has no intention of straightening out the Gothamites with harsh discipline; he intends to radically alter the culture and history of the West, in the same way that Rome's fall marks the beginning of the Dark Ages and Constantinople's fall leads to the internalization of European politics and their eventual imperialization.
The first fight has Bane going all out in proclaiming himself Ra's Al Ghul's heir and successor to the leadership of the LOS, and we have no reason to doubt that he does see himself that way. His biggest competition killed their predecessor, which even Loki notes won't gain you any friends. At no point does Bane actually successfully carry out one of Talia's orders; she only gives him one order and he promptly ignores it. Everything else is part of "our plan."
Talia, on the other hand, has a more personal feud with Bruce, and is less zealous about the League's goals and more viciously trying to punish Bruce for hurting her emotionally. This is a woman who has effectively had her parents ripped away from her in the same way Bruce's were, but where he was denied vengence by Falcone and grew beyond that Bane and into trying to build up his parent's legacy (the same way Bane seeks to build up Ra's legacy), she's already helped her father take revenge on her mother's killers and it's not exactly improved her maturity.
And while Talia does claim allegiance to her father's ideals, for her its all about the payback, baby. Whereas Bane sees torturing Bruce's soul as an added bonus to defeating him and focuses more on torturing the city, Talia wants to watch Bruce's face as she makes his whole life, all his sacrifices, meaningless. Her offer to take him somewhere on her plane takes on a very sinister undercurrent when you remember she's evil; she's trying to get to Bruce before Bane does.
Their overall plan is obviously something they both agree on, but the one detail they do seem to break on is the one that makes their different goals clear: Bane trys to kill Bruce as soon as possible when he believes (correctly) he might still be able to engineer some kind of rescue for Gotham, finally putting Ra's legacy to rest, while Talia wants him to live a few more moments in torture before he dies.