DS1 (and soon DS2) goes to a single sex selective secondary, but went to a mixed ability primary, so as a parent I've experienced both.
These were our reasons for choosing a selective secondary over the mixed ability alternatives:
I like him learning with students who are in the same ability range as him, because they drive each other on to achieve even more. In mixed ability primary he was always top of the class so got a bit lazy.
I like the single sex aspect because it is cool for boys to work hard and achieve. In mixed ability school he was the only boy who was very able, and got teased for it. Being high achieving was seen as a thing for girls.
I like the fact that the subjects on offer are suited to his aptitude: Latin, economics, further maths etc. He has no interest in technical or vocational subjects, and the mixed ability school is more skewed in that direction.
I like the fact that every student wants to be there and wants to learn. He says there is very little disruption in the classroom and high levels of respect for the teachers. In the mixed ability school that many of his friends attend, a small minority of children don't want to be there and sometimes disrupt learning for the rest.
Selective schools aren't the right environment for everyone, but they do seem to work for some children.