The demographics it attracts can massively contribute to the "extras" the school itself is offering though.
Like an IT room vs 15 old/broken/keys missing laptops that everyone fights over.
Like a dedicated PE/Music/whatever teacher rather than the usual class teacher.
Like better facilities due to a very involved PTA /annual contributions.
Like specialised text books/activity books to prep for SATS /tests and not whatever the cheapest phonics scheme is.
Like current, enjoyable and varied reading books rather than biff and chip and the head's old famous five collection.
Like extra events/parental involvement activities.
Like a greater sense of community.
Like a school ethos that the parents want/agree with.
Like
That being said, there's a massive difference between a church school that IS the local school and everyone gets in and a (normally oversubscribed )church school that requires church attendance, baptism certificates, letter from priest etc.
It will depend on the area and the school, whether you get "more" and whether it's worth it.