Short Version: They're pretty similar in that they both support big government if they like the program and don't support big government if the other party likes the program.
Long Version: In general, Democrats want the government to have a "hands off" approach to civil liberties issues such as abortions, marriage/civil unions, lifestyle choices, etc. However, they want the government to fund a minimum wage for everyone (even if they don't work), public schools (even if you don't like what they teach), a pretty large welfare and medical benefits system, an extensive inspection system for "product safety," and they tend to disagree with homeschooling, pre-abortion notification, or any other form of parents openly exercising their right to parental authority. They also tend to want a smaller military.
In general, Republicans want the government to have a "hands off" approach to economic liberties issues such as taxes, workplace safety, minimum wage, property rights, etc, usually on the basis that government isn't good at doing anything. However, they want the government to ban all sorts of things that they consider moral issues, such as abortions, marriage/civil unions, lifestyle choices, etc, while wanting the government to subsidize other things like homeschooling, school couchers, etc. They also tend to want a larger military.