I went to a girls school and a mixed sixth-form, & I think it worked really well. At primary school I had picked up 'boys are better at maths than girls', and had five years to get over that in classes full of high achieving girls. We had some explicitly feminist teachers who could talk to us about navigating the world (relationships, careers etc.) in the course of ordinary lessons. We had enough girls planning on taking physics A level for two planned classes (though many girls moved for sixth form, like me).
I don't think there was any more social unpleasantness than my friends in co-ed schools got, though if your daughter much prefers boys as friends to girls I'd take that into account. My experience is of state schools, so I don't know if the atmosphere in boarding or private schools is different.
I moved to study the IB, but I think the social aspect, getting used to competing with boys in discussions, and responding to the blatant sexism, frankly, was really important before uni.
Lots of my friends at school took part in mixed clubs (scouts, martial arts, etc.), and hung out with boys from local schools in town after school, so we didn't have a completely segregated teenage-hood.
I think you have to decide on the merit of the schools first and foremost, but in a tie-breaker I'd go for single-sex education for a girl.