My suspicion is that the difference has something to do with the role of the welfare state as well — that the benefits of belonging to a religious community are greater in the U.S. than in Europe in part because our welfare state is smaller, and religious participation provides both tangible and intangible forms of security that are more valuable in a society where the free market is more freewheeling and the welfare state weaker. If you're a Christian who prefers the American model, you might say that the Europeans use government as a substitute for God; if you prefer Europe's path to modernity, you'd probably say something about Americans clinging to churchgoing because it's the only protection available against the harsh brutality of our jungle capitalism. Either way, I suspect that this symbiosis between high levels of religiosity and economic individualism is at the heart of American exceptionalism — which is another way of saying that libertarians root for secularization at their peril.This is way outside my wheelhouse, but here's another possibility: Europe has suffered through centuries of devastating religious wars that didn't end until fairly recently. If you live in Western Europe, there's a pretty good chance that you associate strong religiosity with death, destruction, and massive societal grief, not with church bake sales. So whatever you think of religion itself, seeing the end of religious wars, religious terrorism, and massive state-sponsored religious bigotry is almost bound to make you happy. You'd have to be almost literally crazy not to be happier in today's secular Europe than in yesterday's religious Europe.
Religion in America is just a whole different story. Sure, it's caused its share of problems, but nothing even remotely on the scale of what happened in Europe. We still have a pretty innocent view of religious belief here, and this probably accounts for part of the reason that religion is associated with happiness here but not in Europe. Whether that makes us exceptional or just naive I'll leave for others to debate.