I own both, what do you wanna know?
Katana is more comfortable and a better all-around, do-anything binding and is plenty responsive for the Alchemist. Cleaver highback and baseplate are ultra-stiff and the extra metal on it makes it have that immediate response feeling. The Cleaver is no joke, but it's still comfortable and damp. Katana is more comfortable because the softer highback conforms to your boot - Cleaver highback does not conform to anything, so you have to set it up just right - I initially felt some pressure in my upper heel from it.
I've had a Cleaver baseplate break (Rome replaced it) and think it should only be mounted 4x4 for that reason. The Katana has a more flexible baseplate and the asymwrap puts less pressure on it so I don't worry about that one at all.
Cleaver is the Formula 1 car - top of the line everything but like anything that stiff and performant you're going to pay for it somewhere else like comfort or reliability. Katana is a high-performance production sports car. If you genuinely are between the two get the Katanas. If you know you absolutely need a very stiff but still comfy and damp binding, Cleaver. I guess there's something to be said for putting a "pull out all the stops" extreme binding like the Cleaver on a board like the Alchemist, but really either is going to work really well.