Whilst lots of children get top grades every year in an average type Comp, as a proportion of students, it is obviously a far lower number than in a selective or private school.
This means your DD COULD get top grades in the average Comp, but is MORE likely to in the other schools. Whether she WILL cannot be foreseen.
My DC were pretty bright but not exceptional - think 125 type Midyis or Cat4 scores. They went to a selective private school and came out with a long string of top grades. The things I think that helped were the fact that there was stable teaching - people weren’t leaving mid-year and in almost all cases, they had the same teacher through their 2 year A Levels and 3 year GCSE courses. Probably more important was the friendship group. The vast majority were hard workers. I’d say all of the students had high aspirations, even if they weren’t the hardest workers and knuckled down hard at the end and worked very hard. My DC found their tribe of slightly nerdy and hardworking kids. There were heaps of them. It was cool to work hard, to do well, and when the schools talks about grades 8/9 and A/A* as the norm, and those around you are aiming for it, you do too.
People often say you get similar in state selective schools and can get it too in Comps in the top sets if they set in enough subjects. Kids do naturally veer towards those similar to themselves mostly anyway. But I think what can vary is whether there is a critical mass or bright kids who are highly motivated. My kids were swept along with their able and hardworking peers. They wanted to keep up, and success fed a taste for it.
Of course most Comps will have someone or a couple who get all 9s at GCSE. They might have between 10 and 20 getting all 8/9 grades. Will your DD be in the couple who get the top grades….maybe, but probably not statistically. In the selective orivate school, perhaps 25-35 will get all 9s and maybe 75 will get all 8/9 out if a smaller cohort than the Comp. Of course these kids have all passed exams to get in, but having done that, statistically they are more likely to get the top grades in those schools. If you like there is less ‘risk’ than being in the Comp and hoping you’ll be in the top 0.5%, than being in the top half of the independent.
Final thought, re the independent school, they are absolutely not all equal. How selective is the orivate you had a place at? How good are their results? Sometimes they aren’t much better than the Comp or sometimes worse. Unless a child has SEN or other needs which mean private is better, for an academic child and when funds in the family are tight, I’d only pay for a really top school.