There aren’t very many, past those inherent in the genre. I mean, they both have spaceships in them, that sort of thing, but there really isn’t any sort of a “Western” theme to Cowboy Bebop. “Cowboy” is just a generic term for “bounty hunter” in that universe. They don’t have the whole “low-tech frontier” thing, or the Civil War metaphor. There aren’t any real analogues between the characters, either, although I suppose there are some broad similarities between Edward and River, but only if you really stretch.
Although I’ve never seen it, a friend of mine claims that the anime TriGun is actually very similar to Firefly, at least as far as the sci-fi Western thing goes.