Why do AC cords make so much difference?

Because the AC cords and the AC power in general, is part of your power supply, and the power supply becomes part of the signal as it is modulated by the audio equipment to create the sound. It is the foundation electricity that the signal is created from, and if it is infected with crap, then that will become part of the signal.

I agree with Twl 100%. As such, power cords would NOT make a difference if the gear was built to a proper level to begin with. As i've mentioned before, the more susceptible to AC power cord changes your gear is, the more under-designed that it is. Sean
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The better ones do a good job of filtering out common mode noise from electrical and magnetic fields and also filter noise from equipment (digital) to the outside. But not surprising, some of the cheaper ones can do as good of a job, if not better, than some of the more obscenely expensive ones.

...and I absolutely agree that the power supply design is everything, where a well shielded power cord compliments it rather than trying to wrestle it into submission.