The UK version is quite old now, and it was about a UK politician who was trying to become Prime Minister. The US version is updated to be set there, in a fictional US presidency, and is about a Congressman who wants to become Vice President. They address similar themes of the things people will do for power, and neither pull any punches when it comes to sex, drugs, and murder in the pursuit of power.
I was too young to appreciate the UK version, but the US version (starring Kevin Spacey) is just brilliant. I have really enjoyed it, and I am about to watch the second series now.