I don't think there's much difference between the 6 step CR56 and the Kodak E6, but there is a difference between the 3 step kits and 6 step E6. There's also a difference between the one-shot, single use Kodak E6 and the larger cube sizes. Whether or not you actually see these differences depends on how picky you are and on whether you run control strips. there are differences also between any E6 process using a conditioner and stabilizer instead of the newer version using prebleach and final rinse.
fuji tends to shift magenta/green depending on color developer pH. kodak is more yellow/blue. you can adjust this by adding sodium hydroxide or sulfuric acid to the color developer. you can also run a first wash temp lower to cool the film off, or you can sometimes extend the final washes as well.
I've only used 6 step kodak, so I can't comment on the other kits--I do know that even Fuji labs run Kodak control strips.