In my system power cords sometimes makes a difference, but sometimes not.
Been there, done that. Had a guy years ago, had a whole electronics test bench in his basement. He was a variant on the snake-oil theme. He would admit some wires were better, but not much, and insisted they could all be made at home for a tiny fraction anyway. One time he calls up all excited, comes over so I can hear his fabulous wire that he compared and cannot hear any difference between his and the $7k wonder that he was able to somehow borrow. (He would gladly spend $500 on parts but never more than $50 on an actual power cord.)
Anyway, point is, in my system the huge difference between them was easy to hear. I mean it was obvious, night and day. He was floored. Kept saying over and over again, "They sounded just the same in my system! I really thought they were the same!"
Now here's another point. There will be those who will use this to push the canard that this stuff is all system dependent. Hogwash. Only thing system dependent about it is if your system, or ears, aren't up to resolving the differences. Because trust me, the leopard does not magically change his spots.