There is at least one condition of use where anyone can hear the difference between two different speaker wire construction.
In general, this happens when using a power amplifier that is sensitive to excess load capacitance. This happens because excess output capacitance causes the output current section of the amplifier design to slow down, causing feedback to arrive late, which can then cause the negative feedback in the design to actually become positive feedback. This causes overshoot and ringing on fast wave forms, and actually full instability in some cases. This is easy to demonstrate at the test bench.
if one channel of this amplifier is connected to the speaker load with very high capacitance speaker wire, such as the old Polk Cobra Cables, a multiple strand woven wire that traded off series inductance for capacitance, and the other channel with normal 2 conductor zip cord, the the channel using the high capacitance wire will sound brighter due to the transient overshoot.
In a worse case situation, using a power amplifier in which the normal series output inductor have been eliminated, the high capacitance will cause the amplifier to go into full bore oscillation and die. Then not only can you hear the difference, but you can smell the difference too.
Excess cable capacitance is the enemy of music. My advice is to use very well shielded low capacitance cable throughout your system. Excellent technical engineering specifications for cables are not expensive.