What I noticed measuring my 4BSST at the speaker terminals was that different cords effected the response at around the rectifying frequency, that is above or below the 120 full wave frequency. I should mention that the Bryston tested flattest into the real speaker load on its own stock cord. Just sayin'.
In my estimation, there are three main types of cords:
1) Those that try to isolate a bit from the wall wiring; high inductance, higher resistance cords. May or may not be shielded. Tends to reduced sense of mid to upper bass. Often interpreted as "better highs". No spectral difference is seen on the highs though. Ends up in non-eq'd systems with a bit too much mid to upper bass.
2) Those that try to maximise the connection to the wall; low inductance, low resistance. May or may not be shielded. Tend to increased sense of mid to upper bass, sometimes slam, depending on room characteristics. Can also be interpreted as "sloppy " in the bass if the room is already too hot at those frequencies. Ends up in systems that seem a bit lean otherwise. Some amps have a better sense of "control" on such cables. That, to me, indicates poor power supply design.
3) Those that try to filter out noise, be it digital or other RF. Might be combined with cord 1. Good on RF puking gear like digital front ends and so on.
No power cord is going to deliver more power than the Romex in the wall can. 4 gauge power cords are just silly. Hell, so are 9 gauge cords imho.
On Brystons, I use the stock cords because every measurement on the amp was taken, or made, on stock cords. If I want the Bryston to sound like the Bryston I use what the factory tested the amp on!