The Mead is a private company, ultimately owned by another parent company (Wishford Schools) as opposed to Rose Hill's not for profit, charitable status.
Pros and cons of both obviously.
You could say that The Mead has potentially greater resources behind it as it is part of a bigger group, whilst Rose Hill is standalone, making the Mead possibly more viable.
Equally a quick check of The Mead's 2024 accounts shows that they are owed £3.2m from other companies in the group (up from £2.3m in 2023) and there is an omnibus guarantee across all the schools in the group, making it a target for the bank if any of the other schools in the group fail. Plus it has to be said that the fact that they are profit making adds a different dimension/motive to the school.
Rose Hill, standalone and not for profit, so at least all the resources are ploughed back into Rose Hill. Less weight behind it, perhaps, without other schools in the group to provide support / loans if necessary.
Personally though the not for profit model sits much better with me as a fee paying parent. It's also good to see greater transparency with what is filed at Companies House because as a charitable entity, Rose Hill files full accounts.
As Happywanderer says - different models entirely. I guess the answer is to find out as much as you can about all the schools. Visit them and see/feel which is best for your family. Don't rule any of them out based on rumours from mumsnet or from friends of friends!