Jackfish, the DexIII, an older spec, would be about lowest on the quality of ATF's available out there. It's not even a current licensed spec and usually goes by the name Dex/Merc or DM III, etc. It starts out at a higher viscosity than Dex VI, but will not hold that viscosity as well as the better fluids like DexVI or one of the premium synthetics. DexIII will work ok, but will need to be changed more often than the more advanced fluids.
The synthetic DexIII mentioned earlier would be a much better quality fluid than regular old conventional Dex III. Usually the synthetic fluids or blends are actually now universal-type fluids that are recommended for several different specs, including the older DexIII spec.