Nostress, no, I'm not talking about Pates. I wouldn't send a child of mine to an exam factory (my child is only 5, but the intensive coaching you need to get a child in worries me - even if the school isn't intentionally pushy, parental attitudes will be likely to make it so, and what about the kids coached who are then failures at 10/11?). But Balcarras and Cleeve are brilliant comps, both rated Outstanding, Bourneside is also very good, and at primary level you're pretty much spoiled for choice - there are so many really brilliant primary schools all over town. There are wonderful state schools in this neck of the woods at all ages, even leaving the grammars aside.
Bristol is very, very cheap compared to Cambridge or Bath or London, so it all depends on what your frame of reference is, I think? But the schools I know of aren't great, no. A lot of Bristolians seem to send their kids to grammars in Gloucestershire, in fact.
But as the OP's DH has a job in a nice part of South Brum, and family there, and it ticks all the boxes too, it's a bit of a moot point really!