Which power cord more important?

You should try to demo before you buy. I just demoed over a three week period a shunyata diamondback and a ps audio perfect wave ac10 on my Plinius 9200 integrated and my Naim cd5i-2. All i can say is, both these cords did nothing for my system. Maybe they needed more break in time but, i could not keep them any longer, i had to return them to my dealer. I am not saying power cords don't do anything, it's finding the right one.

Get one you can afford and try it on the cd first, then swap it to your amp. Leave it where you like it most. I suspect you will hear more improvement, depending on the geometry/connectors/conductors/connections on the CDP.
Ps

Thank you all for your replies, when I finally get around and buy one, I'll be very curious to hear the results...so far I'm a bit of a sceptic but would love to be proven wrong :-) ...

I've found once both ends of the chain are accessorized properly, the middle can stand some looking at too.

My exp does say either and both ends. Which ever is first is first. So what? Pick one and go for it!

Out of pure coincidence I put some onto the amps I had at the time. Then my source got one added to it. Then I added a passive power filter. Then a power cord for the filter.

Then I changed things and did it all over agin, but differently.

Where ever is just fine. Amp first? Fine. Do that.

Eventually, all the ingredients are in the pot, right?

The supply cord to the filter is as key as anything else though. It's 'flavor' will be introduced into anything downstream of it. So in effect, the effect on the amp and it's sound is the combination of it's directly connected power cable, the filter or device to which it is connected, AND the supply cable feeding that filter.

Cook for 200 hours minimum if new, 100 if used, season to taste with software .... feeds reserved seating, and standing room only, as a rule.

i noticed very little when i upgraded my first PC. it was only after upgrading all 4 that the "wow moment" arrived.

connected the first one (PS Audio AC-10)from the 20a dedicated line too my quintet. i noticed a bit of bass extension but that was about it. got another PSA AC-10 for my integrated amp then 2 PSA AC-5's for my transport/dac.

things really came together after that.

i would guess the line from your outlet should be first but in the end....you should go all in and upgrade them all.