It all depends on the application. Matching the powder to the load is important, but the fastest burning powder for a given load (weight and velocity) will generally yield the most complete combustion. It will usually leave less residue, too, if only because there will probably be less of it in the shell to start with. The composition of the powder is another consideration, with many folks considering single-base powders cleaner burning than double-base, and they are often advertised that way; there may be something to that idea, but there are also lots of exceptions.
12 gauge 1 oz target loads do best with a faster burning powder like e3 or American Select or Clays (or many others). Some older powders, like Red Dot, do seem a little dirtier to me than others near them on the burn-rate chart. I really like e3, because I've found it to be very clean, even when loading very-reduced loads like bean bag rounds, and it's very consistent---and it's double base. In shot shell and metallic reloading, there have been lots of new powders introduced with the claim of cleaner burning, and I've tried quite a few of them (partly because the newer powders seem to be more available during various crises). The newer powders do seem to be a bit better in a number of ways, but the trade-off is less load data available.
Again, it all comes back to the application. Unique in a .38 Special target load is justifiably called "flaming dirt"; Unique in a high pressure 9X19 load is pretty clean.