IMHO the purely objective approach fails to capture the essence:
Grownups love numbers. When you tell them that you have made a new friend [Amplifier A], they never ask you any questions about essential matters. They never say to you, “What does his voice sound like? What games does he love best? Does he collect butterﬂies?” Instead they demand: “How old is he? How many brothers has he? How much does he weigh? How much money does his father make?” Only from these numbers do they think they have learned anything about him. [The Little Prince, Saint-Exupéry]
But the purely subjective approach cannot yield credible statements, since, as Alan has pointed out,
My point (again) is that you are not able to draw any valid conclusions that are worthwhile (i.e. as a piece or rational science) unless you equalise the levels and frequency responses exactly and make instantaneous switchovers between the amps. And when you do take the trouble to set up and construct a rational scientific test, those differences that you're sure that you hear and you'd swear on your grandmother's grave are tangible, suddenly diminish to virtually nothing or less.
I'm reminded of the poor parents of autistic children, parents who were absolutely convinced that their autistic child, with a parent's hands on the child's, could communicate using a ouija board. Imagine the joy in becoming convinced that your autistic child could now express her intelligent thoughts. Sadly, several blind tests confirmed that the parents, not the children, were, without realizing it, the ones doing the communicating.
The nature and value of real scientific testing, and blind tests in particular, are severely under appreciated in the general population.