Both dramas revolve around a kind of organisation that influences politics in Japan. Both involve moving from the United States to reveal this connection. In both dramas there is a US-journalist that gets involved with people of these organisations. Generally both dramas give off a very similar vibe.
Although one drama (Chief of Staff) directly revolves around a group of people and their role in the political field and the other drama (House of Owls) focuses more on someone who is pulling the strings in the background, are both similar in terms of theme, plan scheming of the characters and corruption. Both are highly recommendable if someone enjoys a well structured political drama.