Bowl, I think you've hit on one of the crucial differences. MB is interested and cares about people, she sees history as a mosaic of individual fragments of lives and experiences and painstakingly recreates the personal to build a bigger picture of the past.
Starkey likes tales of power. That's why monarchy has always fascinated him. His big picture would be a giant Holbein portrait of the king. His people are pawns with a few knights and bishops. The one person Starkey has always claimed that no one else understands half so well as him and the person who has enthralled him is, of course, that bloated egotistical monster, Henry VIII.
I'm not saying that I haven't enjoyed his books, they are accessible, informative and waspish. But they lack the empathy that a historian such as Beard brings.