There’s evidence the Gyrotourbillon can perform admirably as both a watch and a work of art, based on the first modern Chronometrie competition. It lost out by a point to the simpler Master Tourbillon.
If you do not consider the ease of adjustment and the evidence that the quality of the adjustment and luck play outsized roles in measurable performance, then you can say the Gyrotourbillon offers a performance advantage. In theory.
No doubt, there are many elaborate tourbillon movements that are all show and no go, so the fact that the Gyrotourbillon achieves both is enough to win over my heart.
The way in which the Chronometrie competition met its demise and the absence of sincere disappointment amongst collectors points to a real world where everybody knows the answer, so we’ve all agreed to wrap up the investigation and report that the answer will always remain a mystery.