The most obvious - and certainly the most visible - of the differences between the American and British political systems is that the USA is a presidential system, with the apex of power in a directly-elected President, whereas the UK is a parliamentary system, with the Prime Minister holding office and power only so long as he or she commands a majority of votes in the House of Commons.
In theory then, the American President has much more power than the British Prime Minister - he is the commander-in-chief and has the power to issue executive orders which have the full force of law. However, the constitutional system of 'checks and balances' seriously circumscribes the power of the US President who often finds it really difficult to push legislation through Congress. By contrast, a British Prime Minister usually heads a government with a majority of seats in the House of Commons and the ability to pass almost any legislation that he wishes.
In the United States, the transition period between the election of a new president and that person's inaugration is two and half months. In Britain, the changeover of Prime Ministers is virtually immediate - within hours of the election result, one person leaves 10 Downing Street and within the following hour the successor enters it.
In the US, government is highly partisan with the President appointing to the executive colleagues who are almost exclusively from within his own party. In the UK, government is normally equally partisan with all Ministers coming from the governing party but, in 2010, exceptionally the Conservatives were required to go into a coalition with the Liberal Democrats and grant them 17 ministerial positions.
In the United States, the incoming President and his aides make a total of around 7,000 political appointments. In Britain, the Prime Minister appoints around 100 members of the Government and members of the Cabinet each appoint a couple of Special Advisers, so the total...