Are you sure about that? I wouldn't doubt the cleaner part.
I believe that Clays is quite a bit faster burning than Bullseye, even faster than Red Dot. It does lead to more economical loads (about 3.3g for a max load with a 180g bullet), but it peaks out at about 100fps slower than BE. In fact I was going to experiment with some Clay Dot which is supposed to be Alliant's clone of the Hodgdon powder for low recoil loads.
Correct me if I'm totally off base, but from what I've heard, Bullseye is based off of Unique (some say floor sweepings, which I doubt, but it could be finer ground flakes of Unique with an added coating of Nitroglycerine. I suspect the extra coating because the flakes are more prone to sticking to and discoloring the plastic powder measure hoppers. This makes the initiation faster, but the core burn of the powder the same as Unique which accounts for being able to load Bullseye to almost the same mv as Unique for the same max chamber pressure). In pistols, Bullseye requires about 10-20% less powder than Unique for mid range loads. When allowed to burn completely, equal charges of Bullseye and Unique produce almost equal total energy. 11g of each gives me about the same 1750 fps with a 110g Plated RN bullet in my 22" .308.
I also read somewhere that Power Pistol is based on Unique with finer flakes like Bullseye, but with a retardant to make it burn slightly slower than Unique. This allows for higher charges and higher mv's at the expense of less complete burning of the powder by the time the bullet exits the barrel. The under oxidized burn products produce the pronounced muzzle flash of PP when the gasses exit the barrel. Power Pistol gives just enough added velocity to make the difference for competitive shooters to make power factor if they are on the edge. It is not very economical because you do have to use quite a bit more powder to get there. The muzzle flash can also be a distraction if you shoot indoors or in a situation where you don't want to be blinded by it.