I agree that Clays shoots clean, even at low pressures which is almost impossible with metallic rounds (very possible with shotshells). But Clays and Red Dot are super fast powders which build up pressure quickly. They are excellent powders for low velocity/low recoil rounds because they expand the brass cases to seal off the gases. They are not good powders for medium or high velocity rounds because the peak pressures will exceed the SAAMI specs before you can get that bullet moving.
Bullseye is always listed as a fast powder, but it gets its quickness from a heavy dose of nitroglycerin. The rest of the powder burns similar to Unique and the resulting velocities are similar. You use about 10-20% less Bullseye powder for a similar peak pressure as Unique and you end up with almost the same velocity (within a few fps).
I also agree that Bullseye is more "sooty" than other powders, even at full pressures and complete burn loads (no unburned flakes). My stainless steel Ruger Sevice Six revolver looks like a blued revolver after 50 rounds using Bullseye. However, a couple of minutes with Hoppes #9 or CLP cleans it right off. On top of that, I have not found Bullseye to be a problem with auto-loading pistols, the soot does not appear to build up on the insides of my 1911 or M&P40 even after over many hundreds of rounds between cleanings.
If cleanliness is important, you might try Hodgdon Universal (or what was called "Universal Clays"). It is their competitor to Unique and allegedly meters better than Unique and burns cleanly like Clays.
My favorites are Clays/Red Dot for light loads, Bullseye/Unique for medium speed loads and Power Pistol for full speed loads with a nice light show (flash).