At first, I was confused because I thought that transformers were frying integrated circuits, maybe from using the wrong tap or turns and supplying the wrong voltage to the circuit. Then I realized that ICs were interconnects and the killing was even more figurative.
Okay now, interconnects... What's the transformer wire like (gauge, how it's twisted or arranged, etc.), and what are the interconnects like?
But anyway, except in fantastical arrangements or maybe having some EMC issues or some RF getting in, different interconnects should all have very minimal impacts on signals passing through at the frequencies and levels used in audio between different devices. Thus, the sound going into the ears should be almost identical, and you really shouldn't expect to be able to reliably distinguish between different types. That is, except maybe for connecting phono cartridges, where you want low capacitance for some reason I don't quite remember.
One thing to note is that for interconnects, they're connecting together a device with say tens or hundreds of ohms of output impedance and another with thousands of ohms of input impedance. Thus, the resistance of the interconnect is negligible, even for very long runs and very thin wires. So far as you can talk about advantages and disadvantages, higher gauge shouldn't really have an advantage in that respect. I don't think the inductance really is a factor here; I'm not sure about the skin effect, but as far as I know that shouldn't be a factor here either. Actually, given equal wire separation distance, then a lower-gauge wire has more capacitance I think. I guess if you have a really long run or a really badly-designed cable, you could have a slight amount of high-frequency rolloff from that.
I think. I never really paid attention to this stuff.