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

One might also include OTL. 

Looks….If the amp looks ugly it will play as such. LOL

My experience is that the color of the housing is the most influential determinant. A shiney black case produces less harmonic distortion. And I agree that a good on/off switch can make a critical difference. 

In SET amplifier:

1. Output tube.

2. Driver tube.

3. Coupling between stages (transformers and capacitors).

4. Cathodes (cathode or fixed bias, cathode bypass capacitors size and quality, resistors).

5. Signal transformers quality. Output, interstage, input.

6. Power supply. Fist capacitor quality. B+ capacitors quality and size. Voltage stabilization. Power transformers and chokes.

I had a 300b integrated SET amplifier from 2005.

I tweaked a lot of different things:

1. Interstage capacitors.

2. Tubes working points.

3. Cathode and load resistors.

4. Power supply capacitors. Including increased value of capacitors from 100uf up to 3500uf per each tube b+.

5. Cathode capacitors. Including increased value of capacitors from 100uf up to 100000uf.

6. Added interstage transformer for driver and input tube.

7. Added a separate power transformer for drives and input tubes.

8. Build a new 300B SET with external power supply.

9. Changed driving tube from 6f6 to 6v6 and 6L6.

10. Changed output transformers.

I didn’t try to do:

fixed bias, voltage stabilization, SRPP, choke load (LC coupling), direct coupling and many other things.