I can't help but notice that you yourself did compare them in your first paragraph. And you were right to do so. The history plays were very popular in their time, and the Henry VI plays apparently made his name as a young playwright.
Sure, he's handsome and ambitious and all, but when they met, he must have been a fur salesman. And she comes from a privileged, circumscribed world. Was she slumming? Did he get her pregnant?