Yes, this absolutely IS one of those interesting and hotly debated issues, and yes, I've heard the difference. I've been a musician for 50 years (man, I'm OLD), and about 10 years ago I decided to put together my dream bass guitar system. It took me 2 years, countless hours on the internet and in music stores, and trying various components together until I finally arrived at my super duper stereo bass system.
The manager of our local music store is also a bass player and had followed my quest with interest (I had bought my dream bass from him, but got the amps and speakers else where). So, when I had it all done he asked me to bring it down to his store after hours one night to see how it sounded. He was impressed, but went into the back room and brought out a couple of cables and asked me if I wanted to try something. He said he had a power cable that would make my system sound better.
Well, look, I've been around the block a few times, so I laughed, telling him that was silly, but then said sure, why not. Well, I'll be a son of a gun, but after he hooked that cable going form the wall into the power for my rackmount system, I actually heard the bottom end tighten up and become clearer, and it was like lifting a veil off the top end. I was flabbergasted. He went back and forth quite a few times, not telling me which cable he was using, and I would listen, then tell him which one I thought it was, and then go look and see, and I got right every time.
It's one of those things that unless you hear it yourself, you just won't believe it, and trust me, I understand completely the skepticism of anybody out there that thinks I'm either a duffus or lying. But it was quite obvious, not subtle at all.
So........ I'm already using a very good cable going from my bass to my rack system, but he brings over the other cable, which is unlike anything I've seen before, very light weight with metal braiding on the outside. Hmmmmm. It's got arrows on it showing which way the signal should flow, so I plug one end in my bass and the other in my rack. Damn, it tightens up the bass even more, and lifts another veil off the top end. I'm just speechless at this point, so we unplug his two "magic" cables and I go back to my regular (high quality) cables, and now it sounds mushy, which I hadn't noticed before, but now I do. So I plug the new cables back in and the sound is golden.
Needless to say, I bought both those cables (about $300 for both with a 30 day return period if didn't like them) and used that rig for 6 years playing all over the central coast, and let me tell you, every time I powered that rig up, it not only made me smile, but gave me goose bumps. Perfection, and those cables were the whipped cream and cherry on top of the sundae. Occasionally I would try going back to my regular cables, but after a few minutes I just couldn't' do it and would stick the "magic" cables back in.
I've heard all the arguments about snake oil, acoustic memory, etc. Believe or don't believe. Makes no difference to me. I can only tell you my experience and let you decide for yourself. Happy trails.