From Tom Rees of Epiphenom:

How do nonreligious parents differ from religious ones?
Here’s a study by Bart Duriez from the Catholic University Leuven in Belgium that looks into just that. He quizzed more than 900 secondary school students in Belgium about their religious attitudes and their parents approaches to parenting. He also asked their parents the same questions.
Duriez used a rather nifty measure of religion, specially developed at the Center for Developmental Psychology in Leuven. It separates Christian beliefs along two dimensions: how strong their belief in the transcendent is and how literal (or fundamentalist) their beliefs are.
He measured four different aspects of parenting style: support, regulation, extrinsic goal promotion (i.e., wealth, popularity, good looks), and conservation goal promotion (i.e., conformity and tradition).
So, drum roll … who makes better parents?
Well, it turns out that there was no difference between atheists and strong religious believers on the amount of support given to children, how much parental control there was, and whether the parents promoted so-called “materialist” ideas (extrinsic goals).
But there was a strong and consistent difference on conservation goal promotion. Religious parents were more likely to promote conformity and tradition rather than openness to change. Previous studies have found that a parental focus on goal conservation leads to decreased well-being and increased authoritarianism.
You might expect that fundamentalists were more conservative, but this study didn’t find that. Biblical literalism was not independently related to conservation goal promotion. It’s the intensity of beliefs rather than the parents’ so-called “cognitive style” that matters. Where biblical literalism did have an effect was on materialism—fundamentalists were less worldly.
Previous studies have found a link between religion and parental control, and Duriez and his colleagues speculate that their failure to find the same may be a statistical aberration. They conclude:

… although adolescents of religious parents may be less likely to engage in problem behaviors, this might be accompanied by a rigid and closed-minded functioning.

So, who makes better parents? It depends on what you mean by “better.”