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.

Although I have not experimented with AC cords (for lack of time .. young daughter, and daipers being a key reason) my theory is that cords can make a difference for two reasons :

1) they can act as low pass filters. I believe that for digital components this can be important to prevent the digital component from polluting the power supply of your analogue components (preamp, amp etc). It also helps that the digital component doesn't receive noise.
2) They must allow free flow of potentially large amounts of current to the power amp.

I can quite understand why power cords might be good in different applications : a CD transport might benefit from a cord with tons of ferrite to prevent it from modulating noise back onto the power supply. This cord might strangle the dynamics of a power amp that requires large bursts of power.

Ultimately I agree with Sean that if a power supply is built correctly the device should have enough reserve current and should not be either susceptible to incoming noise, nor radiating its own noise back onto the power supply.

Interesting theories ... I hope that potty training will soon give me some more time to experiment.

I've come to believe that the quality of dielectric used can have a bearing on performance, in addition to shielding and current capacity. Hence I'm a fan of well-shielded all-Teflon designs. Write me for details if you wish. Cheers.