Hmmm, essentially comparing a "half aged" tire versus a new shaved tire? I would have to think that the new shaved would always outperform, either by a little, or by a lot, depending on how aged the old tire is. But that's based on the conventional wisdom.
As an anecdote, I put a LOT of heat cycles on the PS2s on my GT3 when I first got it. After 25-30 track days, they had <10k miles, ~50% tread still left (wasn't driving the car hard yet), although they were more like ~1-1.5 yrs old and not <6 months. Car was garaged when not going to the track, so UV degradation shouldn't really be a factor. But I can tell you with that many heat cycles at that point in their lifecycle, they were hard as rocks, you could easily feel the difference in hardness when touching them. Those would obviously be expected to perform much worse than a new shaved set of tires, but this is an extreme. So maybe to tighten up the description of the older tire, maybe you would need to define it as worn down to 50% by "street" use without significant track heat cycles?
Conventional wisdom would say that the half aged tire should not outperform the new shaved tire. If not aged a lot, the older tire could perform close to the new shaved - but seems doubtful it would be better.
Oh, and by "new" I assume you mean broken in new, not literally "just came out of the mold and has never touched the road" new.
I'm not sure there is inconsistency, just a lot of variables in play.
Golden Gate BMWCCA - Car Control Clinics
'13 C4S/'12 328i/'04 GT3
Past: '09 M3 DCT/'03 M3 SMG/'95 M3... missing an E30 I suppose...