Maven would win. She'd hire the Dark Brotherhood to make sure of it.
Yes, but the Dark Brotherhood isn't nearly as friendly toward Maven as she'd like people to think. After all, they did ignore at least one of her contracts. All of Maven's actual allies are based on "what can you do for me", and those relationships can be tenuous when the tides turn. Even the TG would sever their ties to her if she loses too much influence and they no longer need her.
In a debate with Vulwulf, I think she'd win initially. But a few months down the road, she might be the one to lose her cool if people are no longer taking her seriously.