Well, my son is Henry, so clearly that would be my pick. He's the only Henry around in AZ, but when we lived in DC we knew a ton of Henrys. So I guess it's a regional name? FWIW, we named him after my father, so he was getting that name regardless of popularity.
And for a girl, well, I have a Scarlett, so I would go with Charlotte cause clearly I like that sound! We considered Charlotte for her, actually, but knew a bunch of babies born shortly before her named Charlotte, and my son had 2 in his preschool class. So we picked Scarlett, which sounds similar, but is less common. Of course, now I spend my time spelling it for people cause they all think it's Charlotte!