Dexron IV/V never existed. Dexron III(h) is unlicensed, so technically you don't know if what you're getting in that bottle labeled Dexron III really meets specifications - it's up to the consumer to trust the manufacturer of the fluid. TES-389 was Allison's response to transmissions still requiring certain properties of Dexron III and is a licensed fluid which meets the minimum specifications of Dexron III, so if you're hellbent on using Dex III and want to ensure that it meets specifications, use either a fluid which meets TES-389 spec (Mobil ATF D/M does [
see label at bottom of this page], which typically can be found at Target) or obviously Nissan Matic D. I run Castrol Import Multi-Vehicle in my 2001.5 Pathfinder's RE4R01A-HD transmission with a 10oz. bottle of Lubegard Red thrown in, as well as a 19,000 GVW auxiliary transmission cooler and Magnefine in-line filter and things are fine.
Dexron III shears rather quickly from its initial viscosity grade of about 7 cSt. Dexron VI starts out around the same viscosity as Dexron III after it's finished shearing (somewhere around 4-5 cSt, I think?), and GM went through a lot of testing to ensure full backwards compatibility with all previous transmissions specifying previous grades of Dexron - problems may result when certain seal swelling properties of the earlier Group I/II basestocks found in the older fluids were not properly mimicked and leaks may result (
see this BITOG post for further explanation), but this is something of a rarity and Dexron VI should be suitable for most any reasonably modern transmission calling for Dexron III or older. Dexron VI is also a licensed fluid, so even "bottom of the barrel" SuperTech gallon jugs of Dex VI will meet the minimum specifications.
I ran Valvoline MaxLife ATF (which is a synthetic DexVI-esque fluid) for a while and I didn't like its shifting properties in my Pathfinder trans, so maybe there is a grain of truth to it -
however I kind of had a mixture of several transmission fluids in the trans at the time so that is more likely to have caused the erratic shifting.