Reactivating an old thread.
The only function of the power-steering fluid is to serve as a hydraulic fluid. It doesn't lubricate parts under mechanical load. (Such parts are lubricated by moly grease.)
The main difference between Dexron III and Dexron VI is the viscosity. Amsoil lists the viscosity at 100 C for their Dexron III and Dexron VI as 7.5 and 5.9 cSt, respectively. Power-steering fluid temperature rises to about 80 C during multiple large steering movements such as when parking.
Therefore, the main difference between Dexron III and Dexron VI when used as a power-steering fluid will be the steering-effort assist. Since Dexron III has a larger viscosity, it will generate a higher pressure, which will result in more steering assist and less steering effort than with Dexron VI. The difference could be about 10 - 30% depending on the system and particular fluids used.
Other than that, during system tests, the technician will see a different system pressure with the two fluids, which may be somewhat off the OEM specs (too low) with Dexron VI.
Nevertheless, there shouldn't be any wear or damage concerns with Dexron VI.