The headache thing is a load of nonsense imo. The idea is spread by people who think increased purity is going to avoid a headache But all vodka is high purity anyway due to the distillation process.
And I've not seen anyone get vodkas correct in blind testing
Exactly, because there haven't been any medical papers, doctoral theses, or studies on fusel alcohols (also known as fusel oils/accompanying alcohols) and their effects on the human body and brain for over 40 years.
Things like isoamyl alcohol, n-propanol, methanol, isobutanol, amyl alcohol, butanol, propanol, etc., are of course completely harmless and certainly don't cause headaches due to their slowed breakdown in the body.
It's all just propaganda.
I hope my sarcasm is clear.
In fact, these fusel alcohols are not only produced during the fermentation process but are often added intentionally, as they are also used to enhance flavor.
Especially in cheaper vodkas, the methanol content is often over 0.1%. Measurements of 16 grams of methanol per liter (and other substances) have been found in very cheap and counterfeit vodkas on several occasions.
Good, high-quality vodkas are very pure due to the production process and therefore initially very neutral in taste. However, they differ in texture and other aspects, especially in the raw materials used.
I can distinguish cheap vodkas from my favorites in a blind tasting and have won several bets because of it.
Whether the cheaper vodkas differ from each other, I can't say. I tried them twice in my youth and then decided I didn't want to drink them. Every blind tasting or bet since has confirmed this.
But it's similar with wine, vodka, and other alcoholic beverages as it is with audio. In a true blind tasting, the differences are often very small or even nonexistent. Most so-called connoisseurs and critics don't participate in such blind comparisons.