Not much, according to this incisive article on Slate.com: “The existing science is methodologically flawed and ideologically skewed.”
Here is another major point:
…the defensive goal of proving sameness is almost a guarantee of weak science. (The hypothesis that both groups of kids are alike is hard to rule out, but that doesn’t mean you’ve established that there are no differences.) That “heterosexist” bias, Stacey argues, has also encouraged researchers to fudge results, anxiously claiming homogeneity where there’s actually some variety. Why, she asks, buy into the view that “differences indicate deficits”?
And consider the following:
Digging around in the existing data on kids of gay parents leads the authors and others to similarly rosy speculations that these children are unusually open-minded. Some studies, for example, show boys playing less aggressively and behaving more “chastely” as youths, while girls’ early interests are more androgynous and their adolescence evidently somewhat more sexually adventurous. On the hot topic of sexual orientation, the only long-term study of lesbian-headed families reports 64 percent of the young adult children saying they’ve considered same-sex relationships (compared to 17 percent with heterosexual parents)–although the percentage of those who identify themselves as gay, lesbian, or bisexual is the same in both groups.
Here is a survey of some reader reactions.
The bottom line: We need some good labor economists, or demographers, to tackle this problem. That being said, the policy-relevant comparison is not “gay parents” vs. “straight parents.” Rather it is gay parents vs. an orphanage, or gay parents vs. not having been born in the first place. I’ll put my money on the gay parents.