What contributes most to a change in how an amplifier sounds?

The transformer is the beginning to great sound.  It has to handle the requirements of a recording.  If you think about it, why do different amplification from the same manufacturer sound different or handle music differently?  Quick Silver just stopped making one of their amplifiers because they could not source the transformers any longer.  We used to use Plitron transformers but they now require a minimum order of 100 pieces.  Designs are not new so depending on what you are looking for, a design is important to the sound and cost.  Power supply is the key to great sound.  That needs to filter AC noise, handle dynamic swings, etc.  Then capacitors and resistors have an impact.  Tubes vs. SS is personal preference.

Happy Listening.      

@bigkidz , I remember a conversation I had with John Barnes (may he rest in peace) of Audio Unlimited quite a while back.  He was talking about a couple of tube amps and I forget how he exactly worded it, but it was to the effect of when when comparing amps and you separate the wheat from the chaff it is the transformer that makes the difference.

The transformer.

Everyone forgets the power supply. It isn't as sophisticated as the amplifier circuit itself but it's actually the direct electrical connection to the speakers whose impedance interacts with the amplifier to great affect. The thing we think of as the amplifier is basically a valve that opens and closes the power supply supposedly as an analog of the input signal. So the better the amplifier does that the closer the output is to the input albeit larger. But that assumes the power supply is robust and pure. If it isn't even if the amp is accurate it's varying a changing source of current and the result is loss of fidelity.

It turns out many circuits are pretty good but power supplies are expensive and you can cheat with little or no change in the classic measured specs. The only thing that changes with a so so power supply is the sound. Power supply is a major factor why costly amps sound so good. There's money to make pretty good power supplies. But I suspect even 6 figure amps can be improved with even better power supplies.

Distortion signature and output impedance.