I can see bigger wire making a difference in terms of amperage capacity because I know you can trip a circuit breaker by using a cheap thin extension cable for a space heater. I am not sure about tone.
I would like to hear clips of the PS / SP switch.
There are three components to impedance - resistance, which makes up the "real" part of the impedance, and capacitance and inductance, which are respectively the negative and positive components of reactance, which is the "imaginary" component of impedance (using "real" and "imaginary" in mathematical terms).
What you bring up has the do with the resistive portion (mostly) - a conductor of a given cross-sectional area and length will have a certain resistance. Resistance means heat, which, in excess, will destroy the conductor. Conductors of equal length but with different cross-sectional areas will have different resistances - a smaller conductor will have a larger resistance, and vice versa.
When we are talking about speaker cabs in particular, you want a large enough conductor to carry the current of the output transformer secondary. The output current of the secondary is pretty low relative to the capacity of these conductors. For example, from the NFPA 70 (the electrical code), a 14 AWG conductor in free air is at a minimum rated for 25A, which is probably something like 10 times what the output of the transformer is. Of course the NFPA 70 is written with 60Hz in mind, and a guitar amp operates at a large range of frequencies, but it is important to keep in mind that resistance is not a frequency dependent quantity, and as resistance is the component of impedance that causes heating, we can be fairly comfortable that the ampacity of the cable is not greatly impacted from frequency. There are OTHER considerations impacted by frequency but they are not relevant for our application.
So, from a capacity perspective there is no real concern here. Now, on to the tonal discussion - what are the potential impacts to tone? We return to our impedance - all three components of impedance have a potential impact on "tone" as any impedance acts as a filter. Of particular interest are the reactive components of impedance, because they are frequency dependent. That is to say, inductive and capacitive elements have a variable attenuating effect on AC signals that changes with the frequency of the signals.
Here is the thing - the reactive components of a copper or aluminum conductor's impedance are pretty damn small relative to the resistive components. They are more importantly small compared to the reactive component of the SPEAKERS impedance.
Thus, my assertion that these claims of substantial tonal changes between speaker wire are silly. I'm not saying that there is literally no difference - electrically speaking, there definitely is. But as with most things, it is a question of degrees.
