The ST fluids typically compare favorably to the majors, overall, when you look at fluid properties and additives.
John in correct in stating that this Dexron III(h) fluid is no longer licensed (as also is the Mercon of Ford). And as such, there really is no controlling entity to validate the brews. Aftermarket alterntives will be seen as "Dex/Merc" or "D3/M" or such, becuase the full legal licensed names can no longer be used.
However, I've seen info on PQIA that shows the fluids from the majors and reputable houses such as Walmart, AZ, AAP, etc all still utlize a fluid that meets specs that would have been approved under the former systems.
I personally use house branded ATF (ST from Wally, AAP, AZ) and have never had issues when changed under the OEM guidelines. In fact, I've even had a couple used oil analysis done and they were just fine using the house brands.
Here are links to the PQIA info for some recent ATFs tested:
http://www.pqiamerica.com/ATFdecember2012/ATFdecember2012.html
http://www.pqiamerica.com/ATFdecember2012/ATFdecember2012p2.html
http://www.pqiamerica.com/July 2012 ATF/ATFjuly2012.html
http://www.pqiamerica.com/ATF Feb 2012/ATFFEBConsolidated.html
As you can see, they are generally all similar, and are likely to perform well in normal use. Any really poor performers are called out as such; the major names you'd recognize seem just fine.
Even though the standards (Dexron III / Mercon) are no longer licensed, the major players seem to be honoring the system well. There are literally millions upon millions of cars with applications for these two (extremely similar) fluids, and therefore I believe there will be a need for decent fluid replacements in the marketplace for years to come.
Also, Allison has a spec that is essentially a duplicate of the Dex III; it's called TES-389 and there are several brands that do meet that current spec'd criteria:
https://fdlrd.swri.org/Allison/ApprovedFluidsList.aspx?Id=2
One word of caution about GM "back spec'ing" the DEX VI into DEX III applications. In some older Allison applications, there is an issue with the chemistry package of DEX VI and the seals in older transmissions; eventual leaking is very possible. There is a long, detailed, no-love-lost story behind the whole GM/Allison fluid debate, but just know that if you have an Allison made before 2007, it may well be subject to adverse reactions to DEX VI. That is a major reason they then created the TES-389 catagory, rather than accepting the DEX VI, after GM sold Allison. They were forced to do it for about a year or so when DEX VI came out in 2006 while GM owned Allision, but once they split, Allison immiedately ceased the DEX VI approval. Any TES-389 or TES-295 approved fluid would work in a former DEX III / Mercon application. To confound things, it matters on who you talk to; GM or Allison. That is because even though GM sold Allison a few years ago, they kept the rights to manufactur the 1000 series on-highway transmission made in Baltimore, and use that Allison name for that one application in their popular light duty 2500/3500 trucks, and they are filled with DEX VI at the factory. But the Allision 1000 series transmissions made in Indy do not approve DEX VI, even though they are now made with seals that are compatible with DEX VI ...
Ah - corporate bickering at it's finest.