Re: Contrasts between Bane and Ra's
Ra's was sincere at the League's mission: maintaining balance through burning out corruption. His relationship to Bane is that of a savior to a victim. Similar to Bane's relationship to young Talia. We know Ra's threw Bane out because he reminded Ra's of the hell hole where his wife was killed.
Everything Bane presents us in the film indicates that Talia allowed him to take leadership of the League of Shadows so long as she could complete Ra's work. Recall Bane's "I am the League of Shadows." line. Also from the first Bane vs Batman fight, recall Bane's dialogue with Bruce about betraying the League. Now, look at each character's situation. They are remarkably similar. Both were rescued by Ra's. Both were given training. Only Bruce was chosen as Ra's successor. Bane was cast out by Ra's.
Bane's apparent disgust at Bruce throwing away the position he was offered by Ra's, taken with the aforementioned dialogue from the sewer fight indicate that Bane simply wanted to prove himself the better man than Bruce. The worthy successor, if you will. This is furthered when Bane uses Gordon's speech to set himself up as a symbol for those oppressed by the Dent Act (also by giving them leave to take back their city, giving its citizens what was rightfully theirs); its very much like Batman setting himself up as a symbol for those oppressed by the mob's grip on Gotham prior to and during Batman Begins.
Bane shared the jacket-grip mannerism with Ra's. Recall that Ra's plan involved spreading fear gas throughout Gotham, leaving the drugged citizens to tear their city down. Bane never gassed the citizens. Bane never forced them to rise up against the others in the city they believed to be their oppressors. He simply presented them with the means to do so. Bane allowed Gotham to show the world how depraved it could be*; the citizens and freed prisoners did so of their own volition. This allowed Talia a sort of innocence in passing judgment on Gotham; after all wouldn't the city and its people be better off dead? The prisoners and the others whose rose up would be dealt with; the families they tore apart and the people they wounded would be put out of their misery.
By allowing the people to effectively be their own executioners, Bane managed to triumph over Ra's who would've relied on an outside agent--the fear gas--to initiate Gotham's destruction. At the beginning of the second act (I count the 2nd act as everything after Bane breaks the Batman, up until Bruce rises from the Pit triumphant) Bane has proven himself superior to Batman. Midway into the second act he has one-upped Ra's overarching goal of destroying Gotham.
The difference between Ra's and Bane lies in their conviction. Ra's truly loved his wife and was trying to numb the pain of her death. Bane wanted to prove himself the worth successor to the League of Shadows and repay Talia's kindness (returning with the League to rescue him from the Pit) by helping her exact vengeance for Ra's death. Ra's Al Ghul wanted revenge for his wife's death. Bane sought apotheosis. Ironically its the Batman who achieves this through ensuring that the bomb didn't level Gotham.
The above is based on the dialogue and everything we're given in TDKR (the stuff for Bane and Talia, with some of Ra's. Ra's motive for being in the LoS is, of course, covered in BB).
edit: PS, This is a typed entirely off the cuff without any outlining. I appologize if it jumps all over the place.
"Come!" he roared back. "Come kill me, if you can."