Jea48 is correct, power cords are not just power delivery. The measurable differences don't seem to be profound, but they can affect power amplifiers in particular in a number of ways.
First is the voltage drop across the cable. When I saw 40 watts lost in one of our power amps, the voltage drop across the cable was about 2.4 volts. But a cable has to have high frequency capability as well- anyone that knows power supplies knows why- the rectifiers in the power supply only turn on (commutate being the technical term) when the voltage from the power transformer is higher than that of the filter caps.
Now the amp only drains the filter caps a small amount between AC power cycles. So the result is that the rectifiers only commutate on peaks of the AC waveform, perhaps only for a very brief time! So if the cord lacks high frequency capability, the power supply won't charge up properly and you can hear the result, plus you can measure the power supply voltage as well.
ROMEX works surprisingly well, so the real problem is in the power cord, not the wall wiring unless the building is quite old. However it is illegal to use solid core wire in an AC power cord. Thus, the cable has to flex, can't have any voltage drops (the problem areas are often at the terminations, but the cord itself can heat up from voltage drops as well) and has to have good bandwidth.
If the cord satisfies these requirements it will work fine and won't matter what brand it is.