Zargon,
I will attempt to answer your question.
I have eight dedicated 20 amp circuits in my main listening room. These are run from an isolated subpanel. My Ref3 is connected to its own dedicated 20 amp circuit. After running the Ref3 for about 650 hours, I compared the Purist, Stealth, Shunyata and stock power cords. All power cords were previously broken in with about 250 hours of current. Compared with the stock cord, the other cords were significantly better. As for the Purist, it allows the Ref3 to shine, with greater upper and lower frequency extension (about 1/4 octave, according to my sweep tone disc and my Rat Shack sound level meter), much purer tonality, much greater clarity, somewhat greater space between instruments and air, a sweeter yet more detailed presentation, a much darker (quieter) background, and overall more relaxed experience.
I have used these aftermarket power cords both with and without the benefit of dedicated circuits. Aftermarket power cords used without dedicated circuits offer greater overall benefit, but even with dedicated circuits are a significant step up from stock Audio Research power cords.
Your geographic location and power grid anomalies also affect the benefit of aftermarket power cords.