Well the situation is that there technically isn't any such thing as DEXRON-I, II or III, only DEXRON-VI since earlier licenses have expired and are not renewed by GM. The technically correct fluid in this application is DEXRON-VI since that is backwards compatible for earlier licenses.
Sometimes people recommend DEXRON-III fluids since the starting viscosity is higher than for a comparable DEXRON-VI fluid. However, DEXRON-III fluids were allowed to shear down (relatively quickly) to a lower value, and part of the DEXRON-VI specification is for greater shear stability. So in reality the end result is that a DEXRON-VI fluid will retain viscosity better than any DEXRON-III fluid would. DEXRON-VI fluid is superior in every aspect.
There are some exceptions but this would not be one of them.