Talking to my dad and brother, we somehow got into Catholic fertility in the US. After describing a family with five or six kids, it's still fairly common to hear the quip, "Are they Catholic?" I'm aware of the stereotype, though it wasn't formed from actual firsthand experience. The more noticeable distinction I've picked up on is between those who are genuinely religious and those who are only nominally so (or not at all). My dad guessed greater Catholic fertility remained the case today, though maybe not as pronounced as it had been when he was growing up.
Fortunately, the GSS contains relevant self-reported data on the question extending back to the early seventies. The following graph shows the mean number of children among white Protestants and Catholics in the US over time. To avoid issues with uncompleted procreation while simultaneously trying to minimize unnecessary overlap, only respondents in their forties at the time they participated in the survey are included. The question does not specifically inquire exclusively about biological children, but it insinuates as much. A handful of respondents likely included adopted or step children, but the number is probably insignificant and anyway presumably effects both Protestant and Catholic respondents equally:
Looks like the fecundity gap exists and was a bit wider a generation ago than it is now, but over the last four decades at least has not been very significant and is barely existent at all today.
From the view of the churches, though, Catholics do have the upper hand, since among Hispanics in the US Catholics outnumber Protestants by about five-to-one, and Hispanic birthrates are far higher than white birthrates are.
GSS variables used: RELIG(1)(2), YEAR, RACE(1), CHILDS, AGE(40-49)