Again, my info was based on engineering data and that is that!
However this is a cut and paste of the GM service information from a DVD that is about two years old now. Granted this is a few years old, and possibly GM and Borg Warner have changed their minds again, and I'm not even sure if Dex IV is still good; and honestly don't care. (One reason why I very seldom post on this site. But at times I do try and help, but that is getting less and less and less.)
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My personal opinion is that either will probably work and since it is off warranty who cares so long as it does work.
My suggestion is to call a local GM dealer and beg them to pull up the electronic service manual, and pull up the fluid specs for the 2006 Hummer H3 transaxle and see if it is the same as I just posed from 2-year old DVD version, or changed to something else. A dealer pulls up info that can be updated daily via an electronic system and not much more accurate info can be obtained.
AND THIS WILL BE MY LAST POST ON THIS THREAD AND I MEAN LAST!