I have 2 children and have had experience of local Bmth state primary, a fantastic prep school in Poole, BCS prep school for a short time then BCS senior school.
My kids are both at BCS senior and I thinks it is just great. We joined when it was run by the previous headmaster, and the reputation was a bit dodgy. However, the new headmaster is just lovely - hard working and very approachable. Although it is supportive of children with extra needs, they do not tolerate disruption and behaviour has dramatically improved since he came into post.
They have a fantastic drama dept and sport is also excellent, with many academies. It is not pressured academically and is academically non-selective. However, I have bright kids who are well catered for. They might get an extra grade or two if they went to grammar but the all round education they get at BCS far outweighs this. I also think co-ed is soooo important. Wasn’t bothered about it before, having been to all-girls grammar, but seeing the interaction/banter/healthy relationships with boys/girls, I now realise how important it is.
Bit luke warm about the prep school though. Nothing special compared to neighbouring state primaries, great for sport but not much else. Never saw the head, except day 1 and final day of year 6, which is pretty appalling compared to other experiences, state and private. There are better prep schools in the area, so long as you avoid the grammar crammers.
Good luck with your move. Christchurch is lovely!