How does the role of a Prime Minister differ from that of the American President?
In a parliamentary system such as that of England, the role of the prime minister differs from that of the US president in some important ways.
First of all, the prime minister is always the leader of the party that controls the House of Commons. Therefore, he or she never has to worry very much about getting opposition support for his or her policies. The current situation in the US, where Pres. Obama has to deal with a Republican House of Representatives, can never happen in a parliamentary system.
Second, the prime minister is a member of the legislative branch -- a member of parliament. As such, the prime minister can introduce legislation. A US president can only get others to introduce legislation and they may at times (as with Obama and health care) not introduce bills that are exactly what he would like. This is not a problem for a prime minister.