Watch this for CIA vibes: Homeland (the series), Argo (the film), or Zero Dark Thirty. For FBI vibes: The Silence of the Lambs, White Collar, or the early seasons of Criminal Minds. And if you want to see them argue with each other, check out the movie Olympus Has Fallen—it’s not accurate, but it’s entertaining.
One more fun fact: the CIA once tried to use a cat as a listening device. The cat was hit by a taxi. The FBI prefers to stick with humans. You’re welcome.