US politics are a true "duopoly" . There are two options to vote for. Here, in my opinion, are the differences. If you look at the red state/blue state map, which is a map of who voted for whom in the US, what you actually see is that people in cities vote Democrat and everyone else votes Republican. This makes sense, when you think about it.
To me, Republicans are the go-it-alone party. They believe in little or no government, home-schooling, no health care, a free market, no taxes, no unions. They believe that you're on your own, and you should fend for yourself. In the Republican worldview, the only real job of the government is to protect the homeland.
Let me have my gun, my freedom, and stay off my back. And while on social issues, they get a little 'big government' on people, that's because there's an alliance between Republicans and the Religion. It creates a tension in the ideas of non-religious Republicans who don't want the government involved in things like marriage, online gambling, and the drug wars. However, the go-it-alone motif is the perfect metaphor for living in the country. In the country, you're literally on your own.
And that's not so in a city. Democrats, on the whole, are for education, equality, health care for everyone and a social safety net. To put a name to it would be the "we're all in it together" theory of government. It's a feeling people feel in cities. People band together to form an identity in cities: we're New Yorkers, we're Chicagoans, we're Buffalonians. People in cities can see that if the young people are educated, then they won't end up on the streets together. People in cities can see that if there's a safety net, then that person doesn't have to sleep on the street. People can see that a healthy environmental policy would be better for all of us. (Contrast that with the family whose nearest neighbor is a mile away, and you can see why Republicans don't see a problem with the current environmental policies).
The tension between these two demographic experiences are clear, there's a different mentality between a city and 'the country'. And while I clearly understand that there are Republicans that live in cities and Democrats that live in rural areas, the purple map shows that, generally, this dichotomy exists. People who live in cities vote Democrat, and generally, they feel part of a collective group all working together for the betterment of the city. People who live in the country, are predominantly interested in the betterment of themselves. I don't mean that in a selfish way: I mean, they are interested in schooling their own kids, healing their own kids and providing for their own kids. They don't want the government to help.
To recap: Democrats are more likely to be 'we are in it together'.
Republicans are more likely to be 'go it alone'.
In terms of Foreign Policy, the Democrats would be more apt to involve the world community in their foreign policy. This was mocked by Republicans who admit that their foreign policy on anything (Kyoto, Nuclear Proliferation, trade) is based on what is good for the US and only what is good for the US.
But, even at the macro level of the planet, the fact is, we're all in it together.