By 'nursery age' I assume you mean not starting school until at least September 2025 then? (As those starting this September are still technically 'nursery age' now but their application was due in a couple of weeks ago). Apologies, by the urgency in your post I assumed you meant they were due to go this September.
In that case you have ages to come to a decision but you do need to work together, rather than against each other. You can never be sure whether schools will definitely have space as it all depends on birth rate that year. Schools with space in Reception now might be full in 2 cohorts time, when your child starts.
What kind of 'faith' school are you talking about? Many CofE schools can be quite relaxed, whereas Catholic and other faith schools such as Muslim tend to be a lot more focused on religion. I understand why that is causing tension, if one of you wishes the child to grow up as part of that faith wand the other doesn't. For me, the obvious solution here would be non-faith as your child can still value that part of their herritage in a non-faith school (where there will likely be a nice mix of faiths), but it could be harder for them to attend a faith school when one parent is so anti that.
To help you weigh it up and compare though I would also try to look at them both as just 'schools', rather than faith school vs non-faith school. Which one is closer (more scope for local friends)? Is at least one walkable? (always a plus not to have to rely on cars) What extra curriculum activities do they both offer? What are their facilities like? Do they offer breakfast/afterschool club if needed? (Useful to know for the future even if not needed now). How big are they? (Different children suit different sized schools best), What do Ofsted say? (Would definitely be my last consideration but still worth looking at as two 'good' schools is a very different argument to an outstanding vs inadequate).
Definitely visit both though, with your child and ideally with the other parent too if possible so you've all seen both and can make a more informed decision together. Ultimately though, child's needs should come first.