Speaking as someone who got dd into out of catchment school on physical needs (including hypermobility), this is what I would say:
get all the available material together for the initial application- appeals are very stressful and you're much better off never having to do one
everything you say about either school has to be substantiated: have you checked that they would force him to do PE/there would be no alternative provision? have you checked that he would be able to cope physically (e.g. are there stairs)- visit both schools, speak to both heads/head of years, explain your ds' needs and ask how they would meet them
be prepared for the LEA not actually knowing if a school has disabled access: you have to be able to say "yes, I have visited and they have/do not have X"
be prepared for the LEA not being able to think out of their box- our application to wheelchair accessible school for wheelchair using dd was turned down because the school was not on their register of disability accessible schools- apparently, their provision for the visually impaired was not good enough- totally irrelevant for dd
so be prepared to go into detail: this is what my ds needs, this is what X school cannot offer and Y school can
anything you say about your ds has to be substantiated (letters from GP, paediatrician etc)- they won't just take your word
what is the special provision your preferred school could offer for learning difficulties- be very detailed