A visit to this website will provide a quick overview on the claims about gender specific learning outcome debates.The AAUW is a good source for the research on girls. I am ashamed to admit I don't know who the good source is for research on boys.
There does seem to be agreement about one thing regarding girls only education that is of benefit (but which of course has never been researched), and that is girls and teachers of girls report the students have much higher self esteem.
I like the idea of allowing public charter schools to do all boy and all girl schools, so long as they are given adequate resources. It is another way to give parents and students more choice in public education. I wouldn't favor anything more than that though.
Private schools have been segregating genders for some time, and would seem a good choice for research, but I don't know that any has been done.