I like the sound of the other school, tbh. I think giving children the opportunity to make their own decisions and then have to manage the outcome is good. Is your DC bright? If she is, then she won't study much, will she? I didn't do any studying until about 6 weeks before exams, and then I used to do past papers. You've no idea how many repeat questions come up. 19 of the 20 on my A level pure maths were questions I'd done before!
Anyway, I digress.
Religion can be oppressive, but something has triggered her attitude to it, so talk to her and find out what exactly is bothering her. You might be surprised to hear it's nothing to do with religion.
My senior school had only just introduced a uniform when I joined. They allowed us to mix and match across 3 colours - black, navy or grey. It was the school no one wanted to go to; everyone wanted to go to the ex grammar school. Well, that was completely turned around when my year told everyone how great our school was, and that was versus we were treated like human beings, teachers talked to us not at us. It also achieved better results than the other schools in the area, too. There were no ratings in my day, but it was rated outstanding as soon as the ratings came in and is now rated the best school in the area.
How do the two schools do when you compare Ofsted ratings? Are they on par? I assume so otherwise you wouldn't have agonised over which school to send her.
Like I say, find out the real reason she wants to leave before deciding, but imo there is nothing wrong with giving children the ability to decide their own destination. Education and results can come later, noone needs to force themselves to take exams etc. When my hubby died my kids stopped going to school because my DD was asked to write a eulogy as if her father had died and my DS was shouted at by his art teacher asking him where he'd been and he was forced to say out loud his dad had died. My DS has autism. And that was at the best school in the city where we lived! Anyways my DD turned 15 and the course tutor at Get Skilled allowed her to join their programme. She has 5 gcse equivalents, worked at Apprenticeship and has other work experience, which she would not have gained had she stayed in school and is now doing a BTech so she can go to uni. My DS stayed away from mainstream school, he found it difficult. But he was eventually given 3 hours a week homeschooling, and he got 5 GCSEs on no study (he is very bright, but he only properly went to school until he was 11 years old, so 5 gcses off that is a mean fête). He's now an apprentice, and this week, his college principal nominated him to be interviewed on camera by the BBC. I'm not sure when it's airing, but the reporter suggested he went into politics!
So you see, kids find their own way. I am 100% behind good education, but not everyone learns at the same rate or in the same way.