Most European countries, mostly due to their proportional representation electoral systems and/or strong regional political differentiation, have more viable political parties each at the national level than the United States, which has just two viable national political parties.
Overall, in general and on average, European countries have a political center (median set of policy views) that is discernably to the left of the American political center. In substantial part this is because they have wider electoral participation (ca. 90%+ v. ca. 50% eligible voter turnout in top of the ticket elections), in part because their electoral system makes everyone's vote count much more palpably, and also because they did not have strong franchise limiting factions in the post-WWII era when the franchises were set. But, they also lean left for historical reasons: the leveling effects of World War II, the Nazi movement's defeat's effect in discrediting the political far right for a while, and the sense of shared collective purpose that followed from the need to rebuild after World War II.
But, the multiparty systems of Europe also mean that political extremists, such as Communists (as opposed to Center-Left Socialists and the Labor Party), Fascists or Neo-fascists (as opposed to Center-Right Christian Democrats and the British Conservative Party).
Europe also has more separatist parties. This is due to stronger and more ancient regional identities, often with their own languages, compared to that of the United States. It is also probably due in part to a lack of federal institutions that can sufficiently satisfy separatist urges.
The supermajoritarian features of the American living constitution (e.g., separation of powers, judicial review, Senate filibusters, bicameralism, staggered Senate elections, federalism, Senatorial privilege in judicial appointments), also heightens the political power of politicians in the muddy middle relative to political extremists, in a way not nearly so true in strongly majoritarian unitary parliamentary systems. The path to real power in American politics is ultimately through moderation and not extremism, although there are still fewer moderate elected officials than there are moderate members of the enfranchised population. More accurately, the path to political power in the United States is through moderate partisanship as opposed to extreme partisanship.
A very weak tradition of direct action in American politics (e.g. general strikes, insurgencies, assassination, huge street protests) relative to our European peers also weakens the power of extremists in our political system. Then again, this may put cause and effect backward, the political weakness of extremists may be an important source of a weak tradition of direct action in American politics.
The not quite consensus in academic political science and on the political left is that a European multiparty system created by European style electoral and constitutional institutions would be preferrable to the American political system. But, would the cultural price that American democracy would pay in legitimatizing a much wider range of ideological extremism really be worth having a set of politicians who more precisely and unfettered by political party history match the views of the voting public at large?
There is, of course, middle ground. One could ease up the constraints of our election laws in a way that naturally favors three or four political parties, rather than just two. This would open the door to less extremism than the kind of political systems of Europe that naturallly gravite towards five or six political parties, let alone an Israeli style nearly pure proportional representation system that allow a panopoly of tiny parties to flourish. But, whether one expands the number of parties that the electoral system can naturally support from two to four or to twenty, the trade off between legitimatizing political extremism and providing more choice to voters, represents two sides of the same coin. They are almost inextricably intertwined with each other.