I've seen The Dark Knight Rises three times. The first time was in theaters, the second was part of a marathon at home with all three movies and the third was standalone where I just analyzed the movie. The following comparisons are taken from that third viewing.
In the opening scene of the movie Bane has a line where he says "Nobody cared who I was until I put on the mask." Essentially the mask is less a pain reliever (as many assume) and more of a way of becoming a symbol of fear, much like Bruce Wayne did with Batman. When he puts on the mask he becomes more than the man he was before. Now he's BANE, not just a person but a symbol. He really is the evil version of Batman when it all boils down.
Both Bane and Batman had the same training. One was trained by the league of shadows and left because it went against his moral code and the other was kicked out for being too extreme. In a way they both had the same beginning but took separate paths at that juncture. Bruce Wayne left with the training but also with the need to fight the type of people who would corrupt others. Bane left with the training but with the extreme need to corrupt and destroy.
They both also use hope to aid their overall plan and purpose. Batman uses hope to inspire people to stand up and become better. Bane uses it in a similar way, but only so they will fall even farther in their final moments. Batman uses his symbol to inspire true hope, while Bane uses it to create a false hope, a mockery of hope.
They're also both drawn to the darkness in similar ways. Batman is drawn to the batcave because it's what he fears. If he can embrace that fear he can be invulnerable in his mind. Bane lives under Gotham, in the sewers. A very similar environment, but with a different effect on him. The sewers represent the basic structure of which man builds upon. The purpose of the League of Shadows is to tear a structure or town down once it gets too big and out of control. It makes sense that he would put his base at very bottom.
After analyzing the character and his parallels to Batman, I've decided that he might actually be my favorite Nolan Batman villain. He's the Faith to Batman's Buffy. The Silva to Batman's Bond. Two men who mirror each other in almost every way but managed to end up on opposing sides.