If Cables Are Not Tone Controls...

I don’t think you will get a unified consensus on your query. I am in a camp where I want my cables to be transparent so my music is reproduced with as little or no coloration. To answer your question about choosing one set of cables over another is more to do with ‘synergy’ than tone controls found on a preamp or integrated.

@chayro

You accomplish this by listening. Listen for the differences between recordings, and even from track to track on the same recording. The more similar all the tracks sound, the more the cable or component is imposing its own "sound" on the music, and thus the less transparency. Conversely, the more differences you are able to hear, the less the cable or component is overlaying its own sound (often referenced as ‘house’ sound of a component or cable) and the more transparent it is to the source material.

In your example above, you said ‘I have a pair of speakers that I did not like, but were transformed with different speaker cables’. I think what has happened here is second set of cables took away a ‘bad thing’ like harshness or something else you were hearing with first set of cables. In this case a cable change led to more transparency. Now you are hearing a sound (mind you from same components) is more like it should be :-)

+1, @douglas_schroeder