I had a brief class in college that dealt with the exactly the question you posed ...Both do sound "scientific" and perhaps even "objective" but both falter on the same question: how do we know the reproduction is close or far from the original? Do we know the original (even the one on the recording) actually sounds?
Belive me thats a rabbit hole you dont want to go into.
For this discussions lets assume that
"You cant rerecord the performance and therefore this is the only source you have."
The only practical question at hand is if the subjective effects can be attributed to the measurements we have ....
Since there are no amplifiers that are *rated* (not described), wrt depth or other euphonics, i guess there are no reliable measures of those.
I wonder why warm cant be measured though ...that is now understood as caused by the tube distortion and iam sure the quantity of that can be measured.
In any case, i do understand from the responses here that there are folks who extremely care and believe they can distinguish the euphonic qualities arising from amplification alone. Therefore for these folks these measurements are immaterial unless those euphonics can be demonstrably achieved.
I get it. Thank you. That was the question i had asked. I guess its been answered.