Importance of Power cords feeding Conditioners

My question, if this is true and it seems so to my ears at the demo, that it is, is it equally true for all power conditioners? In particular, I am using a Pure Power APS 1050 regenerator.....

it seems that it is just as important for AC regenerators as well. The reason is that AC regenerators regenerate the output AC sine wave using electronics (called a power inverter) that runs off DC power that was created using the AC from the mains/wall outlet. Without bogging you down in too many details, inside the AC regenerator there is a sine-wave generator that runs off DC (created from the AC from the wall outlet) & this sine wave is fed into a power amplifier that amplifies the voltage to 120VAC & also provides the capability to supply several Amperes of current (that your CDP, DAC, TT, preamp, power amp, etc, etc can use). This power amp is also running off DC (created from the AC from the wall outlet). So, if you end up using an el-cheapo AC power cord & you have distorted AC going into your AC regenerator, then, the electronics inside will run off a corrupted DC power supply which will show up as less than the best sonics possible. So, use a better/best power cord within your budget.

Power cords on conditioners is indeed important , and matching that cord to your unit is of the utmost importance . I tried many power cords on my Shunyada V-Ray , all of similar girth , it was there rather pricy Anaconda that rang my bell .
We used to call it the humpty dumpty affect , if you don't get things right at the beginning , nothing you can do will put things back together .

I just upgraded my two generations old BPT top of the line power cord, to their current top of the line, on my BPT power conditioner, ansd was quite surprised at the degree of improvement.

As promised, I checked a range of cords on my Pre Power APS 1050 regenerator. I picked up a Nordost Valhalla and Virtual Dynamics Master 3, quite cheaply, over the last couple of weeks;

System used for test Leema Antilla CD Player
Pathos Inpol2 integrated amp
Pure Power 1050 Regenerator
Virtual Dynamics and Silver audio
interconnects
Virtual Dynamics revelation SC
Music used
Lyle Lovett Joshua Judges Ruth Tr 4
Dvorak Russalka on Decca with Rene Fleming

First up, the generic, thick copper PC I have been using for years. Cost abot $30, no comment on it, used as baseline

Nordost Valhalla: A crisper, cleaner sound, more dynamic, a bit more detail heard on the recordings. I thought the soundstage lacked depth and the sound a bit clinical. So better, but not by much.

Lessloss DPFC Origonal: A bigger step up, the same improvement in dynamics and detail, but sounded more natural a better musical flow, definitely more enjoyable

VD Master mark 3; Very similar to the Lessloss, but with better base grip. More enjoyable for that.

So there clearly was a difference and the Lessloss and Virtual Dynamics were about equal in quality, though I preferred the VD. I would say there was not as much difference as putting the same cables on the amp or CD player, perhaps that is accounted for by the Pure Power being a regenarator, not a conditioner. If I had one, it might be interesting to repeat the comparison with a conditioner, but I don't have one.

So that's what I found.

I disagree that the PC to the conditioner is most important. The most significant I've found is PC to source. I have noticed differences w PCs to conditioner, true. But not nearly as dramatic as PC to source.