Before an impressionist can get a good impression down they have to zero in on the traits that make that person recognizable. For example, Tarran Killam, who does Brad Pitt on Saturday Night Live, has said that his Pitt impression takes the stoner-surfer drawl that Pitt used in Se7en and combines it with the hand gestures Pitt used as an unstable maniac in 12 Monkeys. Pitt has made a lot of movies, but those are two of his more iconic roles, and they are both big performances, so it makes sense that Killam would look at those movies to help him define what "Brad Pitt" is.
It's also understandable that Killam didn't look to Cool World for inspiration. For one, this partly live action / partly animated movie didn't leave a big impression on American culture, so the tics that Pitt uses to create his cop character here are less recognizable than the tics he used in those more well known movies. But more importantly, this might be Pitt's worst performance and the movie itself is insufferable, so Cool World isn't a good place to look, period.
To some extent Pitt's subpar work isn't all his fault. The script doesn't give him much to work with: the plot about cartoon sexpots who want to sleep with human men so they can become humans themselves is nonsensical, and all the sideline characters are grotesque, so Pitt's character is asked to react to a lot of situations that are utterly untethered to real human experiences. And his failure to convincingly interact with the animated characters has to be blamed in part on director Ralph Bakshi, who would have been responsible for giving Pitt the guidance he needed to look like he was in the same place with characters who were going to be drawn in later. It's not Pitt's fault that his scenes aren't plausibly integrated with the cartoon scenes.
However, it is Pitt's fault that his cop character is so stilted and generic even when he's in a scene completely by himself. He doesn't seem to grasp the noir tone his character is supposed to embody. He's supposed to act like a seen-it-all hardass, but he delivers his lines flatly, with boredom instead of world weariness. He's a poor choice for the anchor of the movie, because his failure to flesh out the human entry point into this ridiculous story keeps the entire movie from ever feeling grounded. There are a lot of reasons why this film didn't make the same splash that the similar humans + cartoons themed Who Framed Roger Rabbit did, and the fact that Pitt lacks the plausible gravity that Bob Hoskins had when he was interacting with doodles is high up there.
Pitt is obviously a talented actor, even if he does have a few bad habits he overindulges in, so I'm not trying to smear the guy. Furthermore, every actor is entitled to a few mis-steps in their career, particularly when it's early on and they probably have limited control on what they get cast in. But I am saying that if it's a choice of watching his inspired lunacy in 12 Monkeys or watching his bored stumbling in the lunatic Cool World - well, that's not much of a choice at all.
Winner: The Cat