I can't see the relevance of the outcomes described in the document linked by TalkinPeace, or any anecdotal descriptions by (say) Reception teachers about how difficult or easy non-nursery attenders find starting school.
In most cases children's nursery attendance or non-attendance is due to parental preference. As far as I can see, the children in the EPPSE study were not randomly assigned to nursery or non-nursery groups. I assume that each child's parents chose for him to attend nursery or not. Parents make decisions about sending children to nursery for a range of reasons, but surely one big factor must be whether parents perceive their own particular child is suited to that environment.
If I am right about this, it follows that the non-nursery attenders will include a disproportionate number of children who were never going to thrive in a nursery/school environment, due to their character or their special needs. If children who didn't go to nursery tend to struggle later with adapting to school, that doesn't prove that those children would have done any better if they'd gone to nursery.
(The authors of the EPPSE study report claim to have normalised for such factors, but I can't see how they could possibly have done that. Apart from anything else, the non-nursery attenders were only recruited to the study at school entry!)
I'll use my own family as an example to explain what I mean. My older child was just the sort of kid who could be expected to do well in nursery or school and to enjoy the experience as much as any child would. That's why I sent her to nursery. I expected she'd like it. I knew that she would not be traumatised by it. Years later, she went to school. She was an outgoing sociable child - just as she had been aged three - and found it easy to adapt to school.
My younger child was the sort of kid who would not be expected to enjoy nursery or thrive there. She didn't (and doesn't) like noise, or crowds, or being away from her family, nor does she have an intuitive talent for social interaction. That's why I didn't send her to nursery. I expected nusery would be a disaster for her. Now go forward a few years. With or without previous preschool experience, such a child was not likely to adapt to school easily.
Of course I don't suggest that my older child is representative of all nursery attenders, or that my younger child is representative of all non-attenders. But I do think it very likely that the nursery non-attenders contain a higher than average number of children like my younger daughter. There's no proof that having gone to preschool would have "cured" such children of being a poor fit for school. Perhaps preschool would actually have had the opposite effect, by subjecting them to more stress than is healthy.
Who can say? There's no certain answer. But the person who knows the child best can at least have a good guess at what that child needs.