The first point to remember is that a President is not a dictator, but instead must govern along with Congress. Thus whatever differences exist in what the two candidates intend, the differences in what they can actually do depend on the congressional elections.
That being said, there are clear policy differences between the two men. Romney tends to favour big business and low taxes for the rich, whereas Obama argues for higher taxes on the wealthy and large corporations, and more of a safety net for the poor and middle classes. The Republican platform opposes abortion, even in the case of incest or rape, whereas the Democrats support a woman's right to make her own choices about birth control and abortion. The Republicans are opposed to gay marriage (and other equal rights) for gays, but the Democrats generally support gay marriage. Romney is not only opposed to illegal immigration, but wants to make life so unpleasant for illegals that they "self-deport", whereas Obama wants amnesty for people who arrived in the US as children and have completed university or service in the armed forces, and have no criminal record. Romney said in a video that he does not care about the 47% of Americans too poor to pay Federal income taxes, but Obama responded that he wanted to be a President for "all Americans".