alt Hacker NewsThe Earth is closer but I don't think there's any good argument to say it's actually a binary system. Notably the Earth-Moon barycenter stays inside the Earth, and the Sun-Jupiter barycenter doesn't stay inside the Sun. But barycenters are too easy to get outside of objects anyway.
As I understand it, one suggested "double planet" definition was that the barycenter would have to be outside both objects. Earth-Moon doesn't (quite) satisfy that condition, but for example, Pluto-Charon does.