Democrats believe that the Government is repsonsible to take care of the people and should make laws that protect society at large. They favor a larger central government with broad authority.

Republicans believe that the Government is not responsible for making sure everyone has a job, food, and roof over there head. They believe in the individual's liberty and responsibility to take care of themselves. They believe in smaller government and state rights over the Federal Gov't.

I am a lifelong Democrat, so take this for what it's worth. But I think the basic difference comes down to the philosophy about what government should do. The following includes very simplistic summaries, and many people won't fit into either category, but this is typical:

Republicans in general believe in minimal government. They believe government should provide for the national defense (this includes a large military, secure borders, keeping out illegal immigrants, and a strong homeland security program). With a more limited government, they want lower taxes and less government intervention in their lives and in the market. They are less opposed to religion in government (regarding abortion, displays of religion, etc).

Democrats believe in a more active government. They want government to provide more social services. This includes strong public education systems, social safety nets (social security, medicare/medicaid, unemployment, welfare), and public health care. They want the government to regulate business to ensure a clean environment. They want to regulate business so corporations won't run wild and abuse consumers.

Basically, republicans want a smaller, less active government, and democrats want a bigger, more active government. There are many, many more differences, but these are the basics.

Is this in theory or in practice?

In theory Democrats are for bigger Government. They believe that the Government should provide basic services to people. Along with that, they also believe that social norms should no take away people's rights. ie.) If a society is generally against gay marriage, that doesn't mean gay marriage should be illegal. Does that make sense?

Republicans generally believe in smaller Government. They believe that people have the right to pursue happiness, but that doesn't mean that they have the right to be happy. They also believe that social norms should be law. If people are generally against something (marijuana for example) then it should be illegal.

In practice both parties tend to act the same. Take for example McCain (Republican) vs. Obama (Democrat)- McCain wanted to stay in Iraq, Obama wanted to go to Afghanistan. Bush (Republican) initiated the Patriot act (spying on Americans) and Obama (Democrat) is continuing that.

Which one is better depends on you personally. If I had to choose between them, I'd choose Republican- but if I had more than two choices, I would go with Libertarian.