Emily King and Kelli McGrath at the Family Class Blog have raised the interesting possibility that children oriented toward their opposite-sex parent might better learn to speak the "genderlect," to use Deborah Tannen's term, of that sex. Being bilingual in the speech habits of both sexes should be an advantage if you can keep the difference straight, though it could easily become a source of confusion if you don't. The general drift of the class's comments, though, has been that these two conditions are not really symmetrical, even if they would carry linguistic advantages. "Mama's boy" is a term of abuse in a way that "daddy's girl" is not.
So here is the question: do daddy's girls talk like daddy, and do mama's boys talk like mama? I don't think there is any real science on this, because the terms themselves are not that precise. Here is my first guess, though. Daddy's girls are allowed to be more feminine in that role, because they are under the understanding protection of their fathers. Mama's boys, on the other hand, are not more masculine in that role, because they are not protecting their mothers, since they are still kids. So mama's boys may indeed learn to talk in a feminine way – looking at who they are speaking to, listening to the words said and to the emotions not said, trying to be equal to the person they are talking to, rather than one-up. All of which would stand them in good stead in friendships with women – but may work against them in courtship. This may work well for gay men, but create real conflicts for hets.
On the other hand, my eldest daughter says "All the best girls are daddy's girls." I don't think this is a scientific statement, either, but I ain't fighting it.