I agree, intuitively one would think so. And it's a common misconception. Fresh snow crystals have thousands of tiny sharp edges and much of the traction in powder from a good winter tire is because the tire holds snow in the tread. Snow sticks to snow. A deep lug tire is designed to clear mud easily and is too coarse to hold snow as well as a finer pattern.
True, because the Hakka 9 has studs they market it as "extreme grip". But the studs aren't going to help in deep powder. That's an overall traction rating for general marketing purposes and is not specific to deep snow.
No, the R3 and the 9 use completely different rubber compounds. The 9 uses a new "eco-friendly" compound using canola oil and the R3 uses dual compound rubber with a harder rubber in the base structure for strength and support and a softer compound overlaid on the tread area. This compound is too soft for reliable stud retention on the Hakka 9. And the R3 has "Cryo Crystal 3 particles" distributed throughout the tread rubber compound.
But I can see your mind is made up and I don't care to argue with you. I only mention it to clear up some common misconceptions for those with an open mind. Studded tires are not the ultimate in deep powder unless the situation is compounded by an ice layer underneath and the tire is able to access it. In that case, the studded tire would likely be superior.