I think of Bane and Talia as two parts of one larger character. Technically the correct answer to this question would simply be the resurgent League of Shadows.
For all intents and purposes though, Bane is the main villain of the movie. Not just in terms of screentime, but also in how he's thematically linked to Bruce and the way his more militaristic/oppressive presence trickles down and seeps into the whole tone of the film, similarly to how Ra's and Joker affected the tone of their respective films.
In terms of the power structure, to me the best analogy is that Bane was the COO and Talia was the CEO (another way of saying he was in charge of day to day operations but still reported to her). Or in movie studio terms, Bane was the director and Talia was the executive producer. So calling Bane a lapdog is kind of like saying Chris Nolan was Jeff Robinov or Thomas Tull's lapdog on these movies. Obviously Talia had her role to play in securing the reactor so she was a hands-on CEO no doubt, just like her father. I think the final result is something more akin to a partnership. Talia is the rightful heir to the organization her father led, but she entrusts a lot of it to her idol/protector. She sees him as fit to lead, and in fact needs him to. It's not something she's able to do while undercover as Tate, nor is she the cult of personality that Bane is. Bane is the true symbol of uprising, both in terms of the film and in terms of the LOS.