What children need are the wide range of knowledge and skills that are helpful in having a good life.
I grew up with two brothers, but because of a three year difference in our ages, I can say that it would have been better if we had been closer to the same age - that would have made it more likely that I would have experienced them as peers in a way that would have been more instructive and rewarding. (In more rural or older cultures, or larger families a three year age difference might not have mattered as much.) All in all it is better to be in a family, as a child, where your siblings are your intimate riends.
Because I grew up without a sister, I'm sure that there was more mystery about what girls were all about then there ever should have been. And I paid for my naivety and misconceptions later. All and all it is better to have siblings of both genders.
In today's much tougher economy where it takes two salaries instead of one for most families to survive, all children are getting less parenting.
Any single parent family leaves the kids deprived of some parenting. (But there is a line beyond which little parenting is better than bad parenting.) All and all it is the quality of parenting and how much of it you get.
When a child grows up without a male parent, or without a female parent, there is more that they have to acquire regarding what a man or what a woman is. (We build models in our heads that we use to understand and react to members of the opposite sex, and to adult members of our own sex as guides by which we model and understand ourselves during our younger years).
But I'd say that each of the paragraphs above is of no importance at all compared to growing up with even a single parent of either sex who is both loving, strong and confident in their parenting, see us for who we are and especially the best within us and has reasonable self-esteem. Even a so-called normal heterosexual couple can be very damaging to child if they have even slightly lower than average self-esteem because it will mean they have a range of defensiveness that is like another party living in the house with everyone... and it isn't a good person.
Bill, I suspect that "same-sex" is used only because of a feeling that "homosexual" may still carry a slight negative connotation due to a long history of cultural disapproval or dislike for homosexuals (mostly targeted at gay men) - but that's just my guess.
Side note: As to the benefits of a child having a role model by which they form the very complex inner-model of what a man or a woman is when they don't have such a person as a parent (for whatever reason), I suspect that over time it will be considered a normal (and almost required) part of parenting to seek out and enlist quality role-models for the child - but it won't be as good as full time parents of both sexes because a chosen, part-time role-model won't make visible the full range and sublety of behaviors across as wide a context.)
On a political/legal/natural-rights basis, I don't think any government should be licensing marriages or interfering in adoptions or saying how children are raised (as long as the kid's rights aren't violated) - but I suspect we agree on this.