The key difference between the two mounts is whether or not you’ll be fitting any form of windscreen on the mics. The INV-7 HG is designed to support the mic from the rear, and allows weight to be added in the form of slip-on windscreen solutions (heavier than foams).
The INV-7 is a pure 'cradle' suspension with more complaint Lyres®, and can only handle a foam gag. The INV 7HG MkIII is slightly stiffer.
So ultimately, it depends on how you’re planning to use your mics.
Relevant product information can be found here:
INV-7 HG MkIII