Some people do think it makes a difference: because of the skin effect in speaker wire, especially when you go thicker than 20AWG, significantly more current flows on the outside of the wire for sound in the treble range. Here's an excerpt from TNT-audio: Speaker cables
In reply to:
For all it is worth, the Skindepth for a round Copper Conductor at 20 kHz is about equivalent to the Diameter of a 20 AWG Conductor. At this depth from the conductors surface the current density is 63 %. Hence a 20 Gauge conductor should not experience skin-effect related problems below 20 kHz.
According to this article, the current on multistranded conductors will end up hopping between the various strands, which can be impeded by oxidizing and "grain boundaries" between the strands and affect the sound.
As for the subjective magnitude of the issues: I am sure some people would not notice. However, there are very real differences between various cables, from an electrical standpoint as well as from a subjective standpoint. I am sure that a specific feature like "solid-core," is less important than the overall build quality, and other considerations.