DEX VI is backwards compatible in most every application for DEX III, but there are a few notable exceptions; one being the Allison 1000/2000 series prior to 2007. That is because of a chemistry compatibility issue with regard to the seals Allison used, not the vis itself.
The topic of Vis, in regard to DEX VI and DEX III is greatly misunderstood. DEX VI has twice the vis retention (and also 2x oxidation resistance) than the former fluid. While DEX III will start at 7.x+, it will quickly drop into the low 6.x range, and even down into the mid 5.x range. DEX VI, OTOH, will retain it's vis far longer. So if your ONLY concern is about vis, then you're in the wrong position, as DEX VI will actually fare better over the long term. And again, it will also resist oxdiation much better as well. Only if you know of chemistry issues (and there are only a few that I'm aware of), should you have concern.
And BTW - if a lower starting vis is what you fear, then by gosh don't touch that bottle of MaxLife; it also starts with low vis (6.1?)! And yet people swear by it, while they curse the DEX VI. Just goes to show how bigoted and uninformed some folks are. I'm not saying they are completely interchangeable; I'm just pointing out how single-minded and one-sided some folks tend to be when thinking about their favorite (or despised) lube.