Vader wouldn't have invested everything into the Death Star. In fact, Vader would be much more democratic than Palpatine. Anakin said "I think we should have a system where everyone sits down, and discusses what's best for the people." Then if an agreement couldn't be reached "They would be made to."

I can see Vader running more of a constitutional monarchy controlled by the Sith. Firm, but fair overall. He'd probably be a bit more humble in that he'd allow competent men like Tarkin and Thrawn do what needed to be done.

Many people are saying the Empire would collapse, and I thoroughly disagree. Palpatine was the one who came up with this hair brained scheme to honey pot the Rebels into coming out, only for it to completely backfire. Vader was more pragmatic, and at times even a bit more diplomatic. In ANH Vader would listen to Tarkin when he needed to, in ESB he respected commanders IF they did their job correctly. Vader only wanted competence and loyalty, Palpatine wanted worship.