I don't have dc at any of them, but, from what I hear......
People like Dame Elizabeth as it is smaller. Used to have a Resource Base and a lot of the staff are used to differentiating for children with different needs. I think it's smaller size is what people like about it most.
Harborne Academy I presume is what Harborne Hill changed it's name to ? Never had a good reputation which is so weird given its catchment area. However, i'm going back 8 years or so now since I've heard anything (not really in our catchment area) so I wouldn't want to do it a dis-service with a really old reputation.
Bournville School is one where OFSTED were a lot less happy than the families that attend. I know a lot of families with dc at Bournville who are very happy and felt really cross about the poor OFSTEDs which they felt were unfair and didn't in any way reflect their experiences. A lot of dc have done well at Bournville. It was certainly much bigger than Dame Elizabeth (10 form entry against 4 from when my dc were at the applying stage) which comes with its own advantages and also disadvantages.
Shenley Court used to be a fantastic school many, many years ago, then it went down, down down and hit rock bottom about 12 (?) years ago. Lots of people sold house and moved to get out of its catchment. Failed OFSTED. Poached the HT from Bournville, got lots of LA support and she (the HT) pulled it up by it's bootstraps. Name change to Shanley Academy at some point. Then had a completely new building (opened 2012). I know quite a few families whose dc have gone there and they can't speak highly enough of it. I have been really impressed by some of the systems they put in place. That HT has now gone, but it still has quite a good reputation amongst people I know.
St Thomas Aquinas is a Catholic school. Not a brilliant reputation but not dire either. People do apply from quite some distance, as they are specifically looking for a Catholic school, and they get in, as local people aren't particularly keen to go there.
Sorry, don't know anything about Queensbridge - that seems a bit far from Selly Oak ?