While constitutional scholars can keep arguing if a parliamentary or presidential system of government is better, but to me it is far more entertaining to see a British prime minister facing the members of parliament and answering their difficult questions. It will be quite entertaining to watch the US president having to do the same!
If you plan well, you might as well be able to watch the action in British parliament in London. (Related: Where to stay in London?)
Overseas visitors can attend debates, watch judicial hearings and committees, and tour Parliament during the Summer Opening season. There are some minor restrictions on overseas visitors regarding which events they can attend, but it appears that the British Parliament is more welcoming than similar bodies in other countries.