Wouldn’t “Boyfriend of Grinning Woman” be more passive language than “Grinning Woman’s Boyfriend?” When I was writing my thesis it was drilled into me to avoid passive language whenever possible.
I do not know what you mean by "passive". There are no passive constructions (verb forms with aux is/was/been and perfect participle).
This is simply another way to form the possessive: of foo vs. foo's.