Salman Rushdie offers some interesting thoughts on our differences:
But there is an important difference between Europe and the United States. In Europe, the Enlightenment of the 18th century was seen as a battle against the desire of the Church to limit intellectual freedom, a battle against the Inquisition, a battle against religious censorship. And the victory of the Enlightenment in Europe was seen as pushing religion away from the center of power. In America, at the same time, the Enlightenment meant coming to a country where people were not going to persecute you by reason of your religion. So it meant a liberation into religion. In Europe, it was liberation out of religion.
Having long been entangled with the European monarchies, the Roman See mightily resisted the birth of democracy, political rights for the individual and religious freedom. The Quanta Cura, an 1865 encyclical of Pope Pius IX, is nicely representative of Vatican sentiment:
For which cause the same Our Predecessors, have, with Apostolic fortitude, constantly resisted the nefarious enterprises of wicked men, who, like raging waves of the sea foaming out their own confusion, and promising liberty whereas they are the slaves of corruption, have striven by their deceptive opinions and most pernicious writings to raze the foundations of the Catholic religion and of civil society, to remove from among men all virtue and justice, to deprave persons, and especially inexperienced youth, to lead it into the snares of error, and at length to tear it from the bosom of the Catholic Church...
After continuing with a great deal of windbaggery and lamentation about the need to exterminate reprobate errors and evil opinions that lead to vile, dire pestilence and calamity (aka democracy), His Holiness continues:
Which false and perverse opinions are on that ground the more to be detested, because they chiefly tend to this, that that salutary influence be impeded and (even) removed, which the Catholic Church, according to the institution and command of her Divine Author, should freely exercise even to the end of the world -- not only over private individuals, but over nations, peoples, and their sovereign princes...
He rambles on, but you get the idea.
To Rushdie's point, European democracy was born in opposition to religion. Democracy suffered no similar burden in the US.