Very similar, though they've changed some things for the new series to give it more depth and length. This isn't to take away from the original series since British series are notoriously short (4 episodes per season in this case). I haven't watched all the episodes of the new series but for example, Francis's wife is merely supportive of her husband and the non-profit side story is non-existent in the British series. Also another interesting thing of note, the congressman sleeping with his secretary, in the British series, the secretary is played by a sista and she is a campaign strategist. Plus there are several side stories not in the original series
However, the Machiavellian conniving nature of Francis that is the heart of the series is still there in all its glory
https://www.youtube.com/watch?v=vTSmBYNdKiY