When our son entered the education system aged five, the state sector was the only sector open to us. It will be the case again at age eleven, excepting an unlikely event around which we, as parents, cannot make solid plans.
The state sector in the UK, and the area where we are fortunate to live, has many fantastic centres of excellence, schools which I would be very happy to send my DS to (both selective and non-selective), and luckily we live near several possible ones.
Not everyone can make that claim. Unfortunately.
However, the state system seems to fail the highest and lowest ability range, those racing ahead, and those struggling to keep up. Much has been done to address the needs of the highest achievers (but not nearly enough), but the lowest ability ranges are more often neglected.
I look upon the state and private sector as an outsider, having not been educated in a school in the UK.
The most vociferous critic of the state sector in our house, is my DH, who was educated in solely in English state schools, selective and non-selective.
It always interesting to watch the English justify ideologically a educational choice they could not exercise.
Only the OP, who chose private education for her children and found it did not meet their needs, is any real position to make a comparison.