traditionally, Europeans were told what to believe in, Americans came to American to believe in things of their own choosing.
Of course this is not wholly the case any more, many European countries are as religiously liberal as the US are now. But a strong monoculture exists in those countries still, with the majority of churches being of a specific denomination.
And of course at least on paper many European countries still have an "official religion", usually the one held to by their royal family.
Enforcement of these religions on the population may no longer happen, but remember that the last of the organisations like the Spanish Inquisition were disbanded only a few decades ago (though the Spanish Inquisition was officially ended in 1834, some of the laws under which it and similar organisations elsewhere operated existed well into the 20th century).
Many would flee from such things, often to the Americas. The sacrifice of doing so was high, high enough that it stands to reason that it would be those of very strong religious beliefs would be the more likely to go to the Americas rather than convert (at least in public) to the official religion of their home countries.
Leaving everything behind for an uncertain future in a rough, violent, country, rejected by your friends and family, probably with a death sentence over your head if you give up to return to Europe isn't something for the faint of heart.
And those of strong religious conviction (rather than those who are religious in order to be accepted by their society) are more likely to pass on that conviction to their children.