I think you will have to try to judge for yourself, as all faith schools are different. Some put less emphasis on the faith than some non-faith schools!
We are a science-y family, unmarried, DP is RC but before we had kids and started thinking about schools he hadn't been to mass for years. DC are baptised RC and DS attends a RC school.
Our school put A LOT of emphasis on faith/religion. In KS1 they have 2h of RE/week, 2.5h in KS2, the vast majority of which is RC-shaded. It rarely/never gets bumped off in favour of other stuff; they're more likely to miss maths or English. Plus it colours all the rest of the curriculum too. E.g. music is mostly hymns, a lot of reading and writing gets done around religious topics, the first ever school trip was to the church, learning about our local community meant learning about the RC community, when the topic was 'families' the focus was on 'our catholic family', when they talk about behaviour/friendship issues in circle time it is used to show why kind behaviour is required.
When I mentioned to the teacher that there had been a death in the family, the response was 'We will pray for you.' Children pray 4x/day (morning, before lunch, after lunch, at home time). They are taught the Lord's Prayer and the Hail Mary. Children ask for the class to pray for their sick relatives etc. Assemblies (parents invited) invariably focus on a religious theme, and start with a prayer. Parent info sessions are opened with 'Let's pray together'.
At age 4 DS came home really concerned about the devil, and worrying that I and DP would go to hell (as we aren't married). We had lots of conversations about symbols (that were too abstract for 4yo DS, he chose to believe in concrete 'true' things e.g. a person-like figure of devil who might come visit you) and about how bible stories, though hugely important and influential and a source for learning, are still stories and not 'truth' or 'fact' (again, DS chose to believe in them being 'true').
Now he's 7 and a lot more critical towards things he's told at school. He's starting to think for himself more. Though in his 'personal prayer' that he brought home recently he did say 'please god help me to pray more at home' (which would be very easy to achieve... ;) )
I think faith schools CAN be quite the brainwashing, and at 4 most young minds are still very predisposed to simply believing what they are told. Not all schools are though. And by being steady and constant at home, querying things, being curious, asking the whys, you can provide that alternative mode of thinking, ready for them when they are ready for it. Also you can model how to deal respectfully with people who believe differently to you, whilst keeping up the boundaries. (Respecting their faith does not mean accepting actions as ok in all cases. Someone doing something terrible in the name of 'faith' does not make that terrible thing acceptable.)
Regarding the often claimed better behaviour at faith schools, I do think it can be the case. I'd say that perhaps some of it is due to the selective intake many faith schools have. And some due to values such as kindness and forgiveness being quite likely to be found in Christian schools (though not a given). However religion does not have exclusive claims to morals and values. Some faithful will ask 'but how can you have values without faith?' implying that values must be derived from some axiomatic faith system. But you will know as well as I that you can have 'christian' values without the christian faith. You can derive values e.g. of kindness without having to assume a god. What I'm saying in a roundabout way is, values of kindness etc depend on each individual school and how it is managed and lead, rather than on the faith/non-faith aspect of it.