Who has greater influence on what their children believe - mothers or fathers?

I've been familiar with the claims made by this article (based on 1994 Swiss census data) that fathers seem to have an outsized influence on what their children believe:

If both father and mother attend regularly, 33 percent of their children will end up as regular churchgoers, and 41 percent will end up attending irregularly. Only a quarter of their children will end up not practicing at all. If the father is irregular and mother regular, only 3 percent of the children will subsequently become regulars themselves, while a further 59 percent will become irregulars. Thirty-eight percent will be lost.

If the father is non-practicing and mother regular, only 2 percent of children will become regular worshippers, and 37 percent will attend irregularly. Over 60 percent of their children will be lost completely to the church.

Let us look at the figures the other way round. What happens if the father is regular but the mother irregular or non-practicing? Extraordinarily, the percentage of children becoming regular goes up from 33 percent to 38 percent with the irregular mother and to 44 percent with the non-practicing, as if loyalty to father’s commitment grows in proportion to mother’s laxity, indifference, or hostility.

Today listening to With this faith I thee wed?– A Conversation on Interfaith Marriage with Naomi Schaefer Riley the opposite claim was made. Drawing from an Economist review of her book you find the claim that:

Childbirth tends to bring Americans back to religion, and women then tend to take the lead: children in mixed unions are twice as likely to be brought up in their mother’s faith as their father’s, even when that clashes with the paternalist traditions of religions such as Islam.

I haven't read her most recent book, which makes a similar note on p. 115 and then on page 159 says that children were more than twice as likely to adopt their mother's faith. I didn't see sources for her claim though, and am unclear as to whether this might be projection as to the future path of the kids' lives (or perhaps if this would really be either a result of or create a path towards nominalism).

I'm wondering what the cause difference might be. Is either figure accurate? Is this a generational difference - which might be explainable by church trends such as the "seeker-sensitive" movement or churches emphasizing more some of the particular emphases of female believers? Is there a difference between the Swiss context and the American context that accounts for the distinction?