The only difference between your system and CHEW is what kinds of clues you uncover. Since the PCs are federal agents solving crimes, the clues are lists of possible suspects, motives, and means. The game even recommends a corkboard for keeping track of clues and making connections to build a case against the perpetrators. The CHEW Quickstart comes with a scene-by-scene breakdown of a prewritten case, but also an improv-friendly version that follows a very similar format to mysteries from Bump and ECB.
From a game design perspective, I think the difference between CHEW and Brindlewood is that the former is about deciding what details are relevant to the case, while the latter is about using all the information you have to find the truth. That's why Brindlewood has you count up the number of clues you find, while CHEW has you roll the same number of dice as long as you have a theory. Brindlewood wants you to tie it all together, while CHEW wants you to question whether the weird details are just dark absurdism or not.