WE did exactly this with ds1. He has dyspraxia, dyslexia, sensory processing issues, very emotionally immature/sensitive. probably mildest end of ASD spectrum in reality. Ds1 appears bright, interestedly and enthusiastic but in reception in a class of 30, busy playground of 2-form entry (i.e. Standard size) primary and constant phonics (which he doesn't get) he did not thrive. His behaviour at home was impossible, although perfect at school. He spent a lot of time sitting in corners hiding and avoiding reading and writing. SChool constantly said he was just 'not matching our expectations' and ignored our concerns. I think they thought he was dim and we couldn't accept it. I don't think the school was hopeless - plenty of friends with totally straightforward kids have had no issues, and I'm sure it would have been fine for most kids. We were scared he would start refusing to go and about DS getting turned off education.
Ds1 started a local prep in yr1, now finishing yr3. 1-form entry of approx 16 per class, with teacher and FT TA until end yr4. we still get a lot of defiance and poor behaviour at home and since ds2 was born some sibling jealousy. HOmework is virtually impossible. However, school is 1000% better. THe staff are so flexible, supportive and individual. THis is obviously easier in a class of adult:child 1:8! School recognised phonics wasn't working and gave up on it - DS was reading chapter books by end yr1. writing very slow to improve but he has had lots of 1:1 support and we are creeping along. curriculum is broad and deep, not just English/maths so the focus isn't entirely on the areas DS finds hard. HE loves the detail in the music theory (hopeless musician tho), literature, history, biology etc they do from a young age. DS has been using an iPad and keyboard in some lessons whichever has helped. Has loved the high quality school productions, and I have felt that some things my state school obsessed friends consider 'pointless', like poetry recitals, weekly judo and yoga, everyone however rubbish playing solos in concerts etc has helped ds' social skills and confidence ++.
for a bright, motivated child with parental back up, I think any reasonable school is likely to get good results in all domains. Ds1 is definitely benefiting from his prep school at the moment. some of his uber talented all rounder classmates are probably getting less benefit, even though they will undoubtedly go off to 'better' seniors.
We spent last year obsessing over what to do for Ds2 who starts reception in sept. He doesn't have any of ds1's difficulties and seems 'average and normal'. We decided to send him to our local primary and then consider a move for key stage 2 or even just for secondary. PArtly to save money but also because I do think local schools should be used where possible. However we were thwarted by not being allocated a place at our nearest catchment school, or our second choice. Both are oversubscribed ('good') and we are in the edge of the catchment area. Our allocated school was in a village outside the city (only 2.8miles away) in the opposite direction to ds1s school and our work. Plus no after school club. So ds2 is starting private school in sept as well!
Who knows what will happen!
Bad part is that cost of two at private school means we will never be able to move to a bigger house. We can't have it all though.