This was our experience, too. We put DS1 was in a private school (in US) because DH works there and we got a decent deal - plus, the school pressured us to send DS1, encouraged us, wooed us in fact.
DS1 has ADHD and SPD - diagnosed, we went in with all the facts, gave all reports, made suggestions - and they complained about DS1 (often to his face!) until DS1 was crying and saying he wouldn't go to school because "He was such a bad boy"
and he "couldn't be good there." 
We pulled him from there last march (2015) and put him in the state school, where instead of small class sizes he got a 1-to-1 aide and regular OT sessions to help with his poor fine motor strength, and he absolutely bloomed.
DH works for a different private school now, and they were more upfront about what they could and could not do for DS1, and the private school's SEN co-ordinator actually said that DS1 would do better getting more services in state schools for a few more years than attending there.
This made me respect the place considerably more!
The first private school had falling numbers and wanted to pad classrooms, but couldn't actually meet his needs and ended up destroying his confidence. It was awful.
DS2 is neurotypical and we're thinking of sending him to DH's current private school as the preK will be cheaper than daycare and much nicer, but I'm keeping DS1 at his current local state school until we feel confident that another place can meet his particular needs as well as our local school.