Why do amps sound different?

Kirkus, sounds like he did!

Since a feedback signal is one of voltage, to satisfy the test might be easier than you think. Just place a speaker with a test tone coming out of it about 1 foot in front of the speaker under test and measure the AC voltage that results at the speaker terminals.

Wireless200, Tubes (triodes in particular) are the most linear amplification known to man. There are some semiconductors that are as linear in some portions of their curve, but not overall. Tubes also have a 'space charge' effect, again particularly noticeable with triodes, that prevents immediate saturation at full output. This limits the production of odd-ordered harmonics.

Anyone with an oscilloscope can view the clipping characteristic of any tube amp and see that the clipped waveform has rounded rather than sharp corners- this is a lack of odd-ordered content at clipping.

Due to the linear characteristics, its possible to build tube amplifiers that employ no negative feedback. Global feedback enhances the loudness cues (5th, 7th and 9th harmonics) that the human ear uses- in effect adding 'harshness'. The addition is slight, but our ear/brain system is such that even hundredths of a percent are detectable. Audiophiles use words like 'hard', 'harsh', 'brittle', 'clinical', 'chalky' and others to describe this effect.

So the trick is to avoid techniques that increase distortion, and to do so while avoiding global feedback. That results in an amplifier that can be very detailed while also being very relaxed.

Tvad, it can be (usually not clipping though), but there are other things that can do that that I would think would be more likely. Resonance excited by volume in the system is where I usually start when looking to kill sibilance. Cartridge setup, driver resonance, odd microphonics and cables are a few of the things that I have found to be more common.

Amplifiers and preamplifiers be guilty too so you have to be suspicious of everything.

In my audio experience, the main issue with amps is the unpredictability of how the output characteristics of an amp will affect the acoustical result of the loudspeaker. An effective way to reduce impact of an amp’s sound signature and get consistent and very satisfying results even with cheap amps is to let it drive directly the easy load of the speaker, removing any crossover components downstream of the amp. The influence of cable and connector impedance will then also vanish to almost inaudible levels. You then have to invest in multiple amps and do the equalizing and crossover upstream, but after having heard the results of doing so, you will probably never want to go back to playing the insane, frustrating and never ending quest of finding the "perfect" amp that will blend best in an inherently imperfect system architecture.
/patrick