Honestly, this is where your problem lies. We all know that some schools are better than others in terms of their cultures and teaching environment, but the standard starting point is that all schools are suitable for educating children, or they would be closed. No appeal panel can agree that a school isn't 'good'. Even if it's an RI school, it's still suitable for the education of children.
If you have issues with the way your child is taught, or pastoral issues, or management of SEN/health issues, that really needs to be managed via the complaints system, because, again, an appeal panel can't say "we agree that they aren't treating Tommy as they should do".
So that leaves what you can bring to appeal. Things that appeals panels can consider would be special programmes that a child with a certain characteristic might benefit from, subjects on offer, particular SEN provision that is different to other schools (but not special units that are accessed via EHCP provision), sometimes, rarely, logistics if it's absolutely key (such as proximity to home/hospital for a child with chronic and serious conditions), sometimes physical environment if it impacts disability, rarely location, if putting a child in the allocated school would put them at risk due to personal circumstances.
So what you need to do is draw up a list of objective differences between the schools and see if there's anything that would be a strong reason to allocate that school. Unfortunately, being unhappy with the way the current school manages your child isn't one of them.