The thing is - it isn't as simple as that.
I've been a lifelong advocate of single sex schools at senior level, with the received wisdom that it's particularly better for girls, and the observation and experience of bringing up boys. But I suspect the quality and outcomes of school life are equally dependent on the ethos and teaching within individual schools.
A co-ed school that is acutely aware of the need to work in ways that benefit both sexes equally, using the latest, proven research and well trained, well chosen staff should provide an equally good experience for boys and girls.
But there are other factors ... It's apparent you're looking within or towards the independent school sector. Is a single sex or co-ed independent school less likely to hold at its core attitudes perpetuating misogyny, racism, hostility towards less represented classes or cultures? Who makes up the senior leadership team? Will pupils find imaginative, empathetic mentors amongst the teaching staff? Whose history is taught? Whose art is celebrated? Whose plays are studied? Which firm is engaged to design the new sports hall? What proportion of the black pupils progress to Oxbridge, or conservatoires, or the Slade? All of these considerations need research alongside your original question - even at the most prestigious public schools.
I would probably have begun with a co-ed school from reception, intermittently reviewing the child's experience and needs and possibly changing at some stage, before committing to single sex for senior school. In your position I'd be inclined to switch to co-ed now, until the 13+ move. But it really depends on the quality of the school.