Being both the cat lover and ol' country boy that I am, I already know the answer to that question.
Cat. Final answer. Crows or ravens are essentially simply larger blackbirds and I've seen cats take them out with much difficulty whatsoever.
A better question in my opinion would be, "Cat or Bird of Prey"? In all my years, I have never witnessed a cat/hawk, cat/falcon, etc., fight to the death. It's doubtful that a cat would win most of those, but I did see a housecat kill an adult owl on Animal Planet once, so who knows?