Notably, same-sex relationships, whether between men or women, were far more egalitarian than heterosexual ones. In heterosexual couples, women did far more of the housework; men were more likely to have the financial responsibility; and men were more likely to initiate sex, while women were more likely to refuse it or to start a conversation about problems in the relationship. With same-sex couples, of course, none of these dichotomies were possible, and the partners tended to share the burdens far more equally.
While the gay and lesbian couples had about the same rate of conflict as the heterosexual ones, they appeared to have more relationship satisfaction, suggesting that the inequality of opposite-sex relationships can take a toll.
That's about the result you would expect once you stop to consider the issue, but it's not something I'd really given thought to previously. Of course it's going to be difficult to get a truly apples-to-apples comparison here since same-sex couples are going to vary in some other demographic directions. Serious biological determinsts are going to say that heterosexual couples just can't be as egalitarian as gay or lesbian couples would, but count me as very skeptical that the differences here are all in the genes rather than the longstanding social norms. One could, presumably, look in detail at the differences between lesbian couples and gay male couples to gain some further insights.
My assumption is that as committed same sex couples become more visible, their egalitarian-by-necessity example will start to have more social and cultural influence. And of course it'll be interesting to see what happens as children raised by same-sex couples grow up.