Conspicuously missing are any references to Detective Story--a Japanese detective show from the early 80's. From my understanding reading about the series and watching both shows, Cowboy Bebop is basically a riff on that show, but in space. In turn, Detective Story is based on the gritty American action moves of the late 60's to early 80's (think Steve McQueen). I don't think anyone can deny Cowboy Bebop certain has a particular gritty feeling.
Imho this is why the live action version fails to capture the essence of the original. It is strictly derivative of the anime and not the prior art.