What all this selection comes down to is one thing, really:
You want your child in a focused, disciplined learning environment.
How DC are selected is almost irrelevant. As has been said before, imagine you had a very ordinary 'bog standard' comp (we all know what I mean when I say 'bog standard', so don't pretend you don't!); if you opened a school that had all the appearances of being reasonably funded, with a credible senior leadership team, but where the entry requirements was the parents being able to juggle, those admitted DC are almost guaranteed to do better, because their parents have bothered to take steps to get that DC into that school.
This is why 'Faith' schools do better- you're either of the faith, a practicing member where all major religions teach childhood obedience and elder respect, or you're sufficiently committed to pretend for sufficient years that you'll make sure your DC doesn't mess up that 'opportunity' you worked so hard to give them.
And, if you 'select in', you can very often 'select out'.
My GS's secret weapon was the girls' SM down the road.
Sadly, in many areas, the comps have too much low level disruption, which appears to almost be 'the norm'. We all know it takes one or two DC per class to wreck the lesson. If the lawmakers in power over Education were serious about tackling the under-achievement of so many DC, both the perpetrators of poor behaviours and the victims, they'd come down like a ton of bricks on this behaviour; the DC would go to PRU's, the parents to parenting classes.
However, improving a nation's educational standards requires far more than band-aids at school; it requires a nationally mandated living minimum wage; the banning of zero hours contracts; strong incentives to go out and work; good, affordable childcare; long term, secure, affordable housing.
Bunging in more grammar school won't touch that, the poor children emanating from some environments blighted by these failures being the ones we at present feel the need to shield our own DC from.