They're both trained warriors and studied scholars.
They both share crime-fighting as a life mission, with an almost religious fervor to it.
They're both respectful of laws and custom, but also willing to break the rules for the right cause.
They're both idealistic, prideful, stubborn, determined, and self-sacrificing.
They're both tempered and collected individuals, but also prone to single-mindedness and violence.
They both have a darker side born from their wounded idealism and righteousness that can get quite ugly.
They both can walk the same social circles - him as a industrialist/philanthropist and her as an ambassador/activist.
They're both deadpan sarcastic and have great poker-faces.
Lots of things in common, and none of it superficial. But the best thing is that they're different enough to counter-balance each other and be entertaining together.