My DH and I have experience that shows both sides of the coin. I just scraped through my 11+, went to the local co-ed grammar school where my brother was 3 years ahead, and loved it there. I was moved into the top stream from the 2nd form onwards, and loved learning languages.
My DH just failed. He was given the option to re-sit, but his gran, who brought him up, was looking forward to his wage at 15, so she refused to sign for him to re-sit. He went to an abysmal secondary school, and left at 15 to go in the mill, as his gran wanted. As it happened, he managed to raise himself up later, got a trade, joined the Royal Navy, and even got a good degree later in life.
But with the difference of maybe one or two marks, one of us had a great school, the other a dreadful one. He would have been great at maths and science, too.
A good comprehensive school could have served us both well, but I do believe I would have been far less happy and successful, because the grammar school had zero bullying, and had this wonderful academic atmosphere. There were no problem kids there, no kids with behavioural problems, no kids who would wait outside school to bash you up for being clever (which I suffered at junior school, though I did learn to fight back in the end)
So, if I'd stayed in Yorkshire I would have got my kids to sit the 11+ which that grammar school still provides, and I'd have made sure I tutored them in the kinds of questions they'd get.
As it happened, I put them through the catholic education system here in Australia. In this country, catholics have traditionally been the best educators. Regardless of my atheism, that system served them well, especially as religion is very low key in such schools these days. And my eldest lad teaches at the co-ed catholic high school he attended. It is like a comprehensive - accepts all abilities.